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plot_comparison(y_test, y_pred, 'Ordinary Linear Regression, Test Set')
import os
import numpy as np
import scipy.io
from sklearn import linear_model
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score, confusion_matrix, mean_squared_error, r2_score
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
from IPython.display import clear_output
import random
import sys
After reading and preprocessing the data in the next code chunk, the data from all cells is stored in a population dictionary. The dictionary's keys correspond to the cell names, and the values contain the data for each respective cell.
The values in the population dictionary are cell dictionaries with keys being 'axons', 'green_dFFMeanValues',and 'red_dFFMeanValues':
'axons', e.g., cell_data_dict['CL090_230515']['axons'] is a 1 dimensional numpy array, of which the length is the number of groups and the elements are 1 dimensional numpy arrays consisting of components belonging to the group.'green_dFFMeanValues' is a 2 dimensional 3 by 49 numpy array (each cell has 3 rounds, and each round has 8 directions * 2 time frequencies * 3 space frequencies = 48 settings plus a extra period so in total there are 49 columns), of which the elements are still 2 dimensional numpy arrays with size being 10 by N (N is the number of components).'red_dFFMeanValues' is similarly a 2 dimensional 3 by 49 numpy array, of which the elements are still 2 dimensional numpy arrays with size being 10 by 1 (only recording the data at the soma).root_path = "/content/drive/MyDrive/Fluorescence_Data/FluoData4Fitting_Average"
# Get a list of all the subdirectories: subfolders are viewed as cell names
cell_names = [f for f in os.listdir(root_path) if os.path.isdir(os.path.join(root_path, f))]
# for cell in cell_names:
# print(cell)
# Create a dictionary with default values
default_value = 0
cell_data_dict = {cell: default_value for cell in cell_names}
# print(cell_data_dict)
file_suffixes = ['green_Axon.mat', 'green_dFFMeanValues.mat', 'red_dFFMeanValues.mat']
for cell in cell_names:
print(cell)
file_names = [cell + suffix for suffix in file_suffixes]
path_ = file_names[0] # green_Axon.mat
path_ = os.path.join(root_path, cell, path_)
mat_data = scipy.io.loadmat(path_)
axons = mat_data['Axons'] # array containing nested arrays/sub-arrays
# Squeeze the outer array
axons = np.squeeze(axons, axis=0)
for i in range(len(axons)):
# Squeeze the inner array and convert the data type to 'int'
axons[i] = np.squeeze(axons[i].astype(int), axis=0)
# final axons' length is the number of groups with
# each elements being a nested array of components
path_ = file_names[1] # green_dFFMeanValues.mat
path_ = os.path.join(root_path, cell, path_)
mat_data = scipy.io.loadmat(path_)
dFFMeanValues_green = mat_data['dFFMeanValues'] # 3 by 49
path_ = file_names[2] # red_dFFMeanValues.mat
path_ = os.path.join(root_path, cell, path_)
mat_data = scipy.io.loadmat(path_)
dFFMeanValues_red = mat_data['dFFMeanValues'] # 3 by 49
cell_data_dict[cell] = {'axons': axons,
'green_dFFMeanValues': dFFMeanValues_green,
'red_dFFMeanValues': dFFMeanValues_red}
# Print keys and types
for key, value in cell_data_dict.items():
print("-- * * * * * --")
print(key, type(value))
for key_, value_ in value.items():
print(key_, type(value_))
print("-- * * * * * --")
CL090_230515 CL090_230518 CL083_230413 CL075_230303 -- * * * * * -- CL090_230515 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * -- CL090_230518 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * -- CL083_230413 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * -- CL075_230303 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * --
# print to see data type and size
print(cell_data_dict['CL090_230515'].keys())
print(type(cell_data_dict['CL090_230515']['axons']))
print(cell_data_dict['CL090_230515']['axons'].shape)
print(cell_data_dict['CL090_230515']['axons'][1].shape)
print(cell_data_dict['CL090_230515']['axons'][1].dtype)
print("--------------------------------")
print(type(cell_data_dict['CL090_230515']['green_dFFMeanValues']))
print(cell_data_dict['CL090_230515']['green_dFFMeanValues'].shape)
print(type(cell_data_dict['CL090_230515']['green_dFFMeanValues'][1,1]))
print(cell_data_dict['CL090_230515']['green_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['green_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['green_dFFMeanValues'][0,1].dtype)
print("--------------------------------")
print(type(cell_data_dict['CL090_230515']['red_dFFMeanValues']))
print(cell_data_dict['CL090_230515']['red_dFFMeanValues'].shape)
print(type(cell_data_dict['CL090_230515']['red_dFFMeanValues'][1,1]))
print(cell_data_dict['CL090_230515']['red_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['red_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['red_dFFMeanValues'][0,1].dtype)
dict_keys(['axons', 'green_dFFMeanValues', 'red_dFFMeanValues']) <class 'numpy.ndarray'> (25,) (19,) int64 -------------------------------- <class 'numpy.ndarray'> (3, 49) <class 'numpy.ndarray'> (10, 281) (10, 155) float64 -------------------------------- <class 'numpy.ndarray'> (3, 49) <class 'numpy.ndarray'> (10, 1) (10, 2) float64
Note:
Four cells: 'CL090_230515', 'CL090_230518', 'CL083_230413', 'CL075_230303'.
'red_dFFMeanValues' and 'green_dFFMeanValues' have 49 columns,where the last column should be excluded. They are supposed to have 3 rows (3 rounds), but 'CL090_230518' only has 2 rows.
In 'CL083_230413', elements in 'red_dFFMeanValues' have 2 columns (10 × 2， should be 10 × 1), so 'CL083_230413' is not used.
def plot_comparison(y_test, y_pred, subtitle = ''):
# Sort y_pred and y_test based on y_test
sorted_indices = np.argsort(y_test)
sorted_y_pred = y_pred[sorted_indices]
sorted_y_test = y_test[sorted_indices]
# Plot sorted_y_pred and sorted_y_test
plt.plot(sorted_y_pred, label='Sorted Predictions')
plt.plot(sorted_y_test, label='Sorted Ground Truth')
plt.xlabel('Index')
plt.ylabel('Value')
plt.title(f'Comparison of Sorted Predictions and Sorted Ground Truth \n ({subtitle})')
plt.legend()
plt.savefig(f'Comparison of Sorted Predictions and Sorted Ground Truth ({subtitle}).png', bbox_inches='tight')
# bbox_inches='tight' will adjust the figure's bounding box to fit all the content, ensuring that
# the complete words are visible in the saved figure. Otherwise, the saved figure may not show the
# complete words, e.g., for x-label, or for the long title.
# The default setting can sometimes result in cutoff or clipped text. It tries to include the entire
# figure within the saved image, but there may be cases where the default behavior is not sufficient
# to capture all the content. The default behavior assumes the figure content fits within the predefined
# margins and padding.
plt.show()
# cell_data = cell_data_dict['CL090_230515']
cell_data = cell_data_dict['CL075_230303']
data_green = cell_data['green_dFFMeanValues'][:,:-1] # exclude 49th column
data_red = cell_data['red_dFFMeanValues'][:,:-1] # exclude 49th column
data_axons = cell_data['axons']
# vstack green data
stacked_green = np.empty((0, data_green[0,0].shape[1]))
# Enumerate the elements in the np array and vstack them
for index, value in np.ndenumerate(data_green):
stacked_green = np.vstack((stacked_green, value))
print(stacked_green.shape, 48*3*10)
# group columns of green data
group_num = data_axons.shape[0]
group_satcked_green = np.zeros((stacked_green.shape[0], group_num))
for i, cols in enumerate(data_axons):
group_satcked_green[:, i] = np.sum(stacked_green[:, cols-1], axis=1)
print(group_satcked_green.shape, data_axons.shape)
# vstack red data
stacked_red = np.empty((0, data_red[0,0].shape[1]))
# Enumerate the elements in the np array and vstack them
for index, value in np.ndenumerate(data_red):
stacked_red = np.vstack((stacked_red, value))
print(stacked_red.shape, 48*3*10)
print(np.max(group_satcked_green), np.min(group_satcked_green))
print(np.max(stacked_red), np.min(stacked_red))
(1440, 80) 1440 (1440, 14) (14,) (1440, 1) 1440 27.44283678657392 -9.505092954427656 0.4404603811981394 -0.20703030293882338
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
x_train shape: (1368, 14) y_train shape: (1368,) x_test shape: (72, 14) y_test shape: (72,)
Ordinary least squares Linear Regression.
Linear Regression fits a linear model with coefficients to minimize the residual sum of squares between the observed targets in the dataset, and the targets predicted by the linear approximation.
# Create a LinearRegression object
model = linear_model.LinearRegression()
# Fit the model on the training data
model.fit(x_train, y_train)
# Print the fitted coefficients
print("Fitted Coefficients:", model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", model.intercept_)
# Predict on the test data
y_pred = model.predict(x_test)
Fitted Coefficients: [ 0.18238332 0.02531578 -0.00635457 0.00804224 0.05353301 0.03116835 0.0537527 -0.02884246 0.15593078 -0.02222356 -0.35561745 -0.00680714 0.00230719 0.13282755] Fitted Intercept: 0.021653732432704836
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Mean squared error: 0.0019353809880106538 Correlation coefficient: 0.6012948658925962 Coefficient of determination (R-squared score, R2 score): 0.35909155398992
plot_comparison(y_test, y_pred, 'Ordinary Linear Regression, Test Set')
# predict on train
# Use the trained model to make predictions
y_pred_ = model.predict(x_train)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Mean squared error: 0.001430949267355517 Correlation coefficient: 0.602014551907171 Coefficient of determination (R-squared score, R2 score): 0.36242152070799216
plot_comparison(y_train, y_pred_, 'Ordinary Linear Regression, Train Set')
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- Mean squared error: 1.375 Correlation coefficient: 0.5122173056905833 Coefficient of determination (R-squared score, R2 score): 0.26050420168067223 Mean squared error: 0.9992690058479532 Correlation coefficient: 0.5523810897035312 Coefficient of determination (R-squared score, R2 score): 0.29920737856320834
Linear least squares with l2 regularization.
Minimizes the objective function:
$$ ||y - Xw||^2_2 + \alpha ||w||^2_2 $$This model solves a regression model where the loss function is the linear least squares function and regularization is given by the l2-norm.
# Create a Ridge Regression object
ridge_model = linear_model.Ridge(alpha=1.0) # You can adjust the value of alpha as per your requirements
# Fit the model on the training data
ridge_model.fit(x_train, y_train)
# Print the fitted coefficients
print("Fitted Coefficients:", ridge_model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", ridge_model.intercept_)
# Predict on the test data
y_pred = ridge_model.predict(x_test)
Fitted Coefficients: [ 0.09292852 0.02632221 -0.00377484 0.00723589 0.05272006 0.02001626 0.01107838 -0.02904252 0.07077848 0.02445001 -0.0740123 -0.00528285 0.00239613 0.0037084 ] Fitted Intercept: 0.021077756347462166
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Ridge Linear Regression, Test Set')
Mean squared error: 0.0019590833656456547 Correlation coefficient: 0.5932188323094388 Coefficient of determination (R-squared score, R2 score): 0.3512424255181108
# predict on train
# Use the trained model to make predictions
y_pred_ = ridge_model.predict(x_train)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Ridge Linear Regression, Train Set')
Mean squared error: 0.0014567165980582566 Correlation coefficient: 0.5925651096246126 Coefficient of determination (R-squared score, R2 score): 0.35094054377913975
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- Mean squared error: 1.375 Correlation coefficient: 0.5131657340158112 Coefficient of determination (R-squared score, R2 score): 0.26050420168067223 Mean squared error: 1.0336257309941521 Correlation coefficient: 0.5293271977916442 Coefficient of determination (R-squared score, R2 score): 0.27511282610707866
Linear regression with combined L1 and L2 priors as regularizer.
Minimizes the objective function:
$$ 1 / (2 * n_{samples}) * ||y - Xw||^2_2 + \alpha * l1_{ratio} * ||w||_1 + 0.5 * \alpha * (1 - l1_{ratio}) * ||w||^2_2 $$If controlling the L1 and L2 penalty separately, that this is equivalent to:
$$ a * ||w||_1 + 0.5 * b * ||w||_2^2 $$where: $\alpha = a + b$ and $l1_{ratio} = a / (a + b)$.
# Create an ElasticNet object
a = 0.004; b = 0.00
alpha = a + b; l1_ratio = a / (a + b)
elasticnet_model = linear_model.ElasticNet(alpha=alpha, l1_ratio=l1_ratio, max_iter=100000)
# adjust the values of alpha and l1_ratio as per your requirements
# Fit the model on the training data
elasticnet_model.fit(x_train, y_train)
# Print the fitted coefficients
print("Fitted Coefficients:", elasticnet_model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", elasticnet_model.intercept_)
# Predict on the test data
y_pred = elasticnet_model.predict(x_test)
# It is normal to encounter warning here, because our data is not linear enough
# and not normailized to guarantee a low error/residual, even though we set a very
# large max_iter. But the results is similar to that of ordinary and Ridge linear
# regression. Like alpha = 0 results in the same results as the ordinary linear
# rergession.
Fitted Coefficients: [ 0. 0.0086643 0. 0. 0. 0. 0. -0. 0. 0. 0. 0.0015826 0.00470322 0. ] Fitted Intercept: 0.022844042914220195
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Elasticnet Linear Regression, Test Set')
Mean squared error: 0.002002060573994312 Correlation coefficient: 0.6136636898586912 Coefficient of determination (R-squared score, R2 score): 0.3370103668241261
# predict on train
# Use the trained model to make predictions
y_pred_ = elasticnet_model.predict(x_train)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Elasticnet Linear Regression, Train Set')
Mean squared error: 0.00169819965499813 Correlation coefficient: 0.4970718988854777 Coefficient of determination (R-squared score, R2 score): 0.24334455576550063
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- Mean squared error: 1.3472222222222223 Correlation coefficient: 0.5463431384225381 Coefficient of determination (R-squared score, R2 score): 0.2754435107376284 Mean squared error: 1.1359649122807018 Correlation coefficient: 0.4511357285754583 Coefficient of determination (R-squared score, R2 score): 0.20334181879094793
Mathematically, a power-law relationship can be expressed as:
$$ y = A X^C $$Here, I modify it, shown as:
$$ y = A (X+B)^C + D $$where, $X = \beta_1 x_1 + \beta_2 x_2 \dots + \beta_N x_N$. $X+D$ is a linear regression part. $A$, $B$, $C$, $D$, $\beta_1$, $\beta_2$, ...,$\beta_N$ are parameters to be determined.
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
x_train shape: (1368, 14) y_train shape: (1368,) x_test shape: (72, 14) y_test shape: (72,)
exponent = 5
# Define the model function
def func(X, *params):
A, B, D = params[:3]
# Compute the weighted sum
weighted_sum = np.sum(X * np.array(params[3:]), axis=1)
base = weighted_sum + B
power_result = np.power(base, exponent)
return A * power_result + D
# Create a LinearRegression object
model = linear_model.LinearRegression()
# give the initial params using linear regression
# so that the params are within a reasonable range
model.fit(x_train, y_train)
# print("Fitted Coefficients:", model.coef_)
# print("Fitted Intercept:", model.intercept_)
num_features = x_train.shape[1]
# Assuming model.coef_ is the np array containing the coefficients
model_coefs = model.coef_
# Set negative elements to 0 using np.clip()
initial_params = [1, model.intercept_, 0] + list(model_coefs) # Initial parameter guesses
# model_coefs_clipped = np.clip(model_coefs, 0, np.inf)
# initial_params = [1, model.intercept_, 0] + list(model_coefs_clipped) # Initial parameter guesses, no need to clip -- they can be negative
# Set lower and upper bounds for the parameters
lower_bounds = [0, -np.inf, -np.inf] + [0] * num_features
upper_bounds = [np.inf, np.inf, np.inf] + [np.inf] * num_features
# Combine the lower and upper bounds into a 2-tuple of array_like
bounds = (lower_bounds, upper_bounds)
# Perform the curve fit with bounds
params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, bounds=bounds, maxfev=1000000)
# Print the fitted parameters
print("Fitted Parameters:", params)
# predict on test
A, B, D = params[:3]
weighted_sum = np.sum(x_test * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, exponent)
y_pred = A * sign * power_result + D
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Power-Law Regression (Exponent=5), Test Set')
# predict on train
A, B, D = params[:3]
weighted_sum = np.sum(x_train * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, exponent)
y_pred_ = A * sign * power_result + D
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Power-Law Regression (Exponent=5), Train Set')
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Fitted Parameters: [ 4.80045085e+00 4.59786665e-01 -8.06259505e-02 1.62406349e-01 2.05395713e-02 -6.46997979e-03 8.02623158e-03 4.71472789e-02 1.41261022e-02 6.84355253e-02 -1.31444397e-02 1.25152014e-01 -2.88069940e-02 -3.41807808e-01 -5.43015976e-03 2.17289817e-03 1.07978918e-01] Mean squared error: 0.002115206617715441 Correlation coefficient: 0.5535858181781245 Coefficient of determination (R-squared score, R2 score): 0.2995416433517336
Mean squared error: 0.0014046095993702319 Correlation coefficient: 0.6116841603489208 Coefficient of determination (R-squared score, R2 score): 0.3741575101258072
---- ---- ---- Mean squared error: 1.4305555555555556 Correlation coefficient: 0.5025479155614934 Coefficient of determination (R-squared score, R2 score): 0.23062558356676 Mean squared error: 0.9685672514619883 Correlation coefficient: 0.5699760409688358 Coefficient of determination (R-squared score, R2 score): 0.32073868075804757
# compared with example 1, here only fit A and D.
exponent = 5
model = linear_model.LinearRegression()
model.fit(x_train, y_train)
# now we have: model.intercept_ and model.coef_
# Print the fitted coefficients
print("Fitted Coefficients:", model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", model.intercept_)
# Define the model function
def func(X, A, D):
# Compute the weighted sum
weighted_sum = np.sum(X * np.array(model.coef_), axis=1)
base = weighted_sum
power_result = np.power(base, exponent)
return A * power_result + D
initial_params = [1, 0]
# Perform the curve fit
params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# Print the fitted parameters
print("Fitted Parameters:", params)
# predict on test
A, D = params
y_pred = func(x_test, A, D)
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Power-Law Regression Exponent=5, only fit A and D, Test Set')
# predict on train
A, D = params
y_pred_ = func(x_train, A, D)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Power-Law Regression Exponent=5, only fit A and D, Train Set')
Fitted Coefficients: [ 0.18238332 0.02531578 -0.00635457 0.00804224 0.05353301 0.03116835 0.0537527 -0.02884246 0.15593078 -0.02222356 -0.35561745 -0.00680714 0.00230719 0.13282755] Fitted Intercept: 0.021653732432704836 Fitted Parameters: [3.72739959e+03 1.69773472e-02] Mean squared error: 0.004292115813928243 Correlation coefficient: 0.31133355789287526 Coefficient of determination (R-squared score, R2 score): -0.4213497463502507
Mean squared error: 0.001824109788677633 Correlation coefficient: 0.43271655960841493 Coefficient of determination (R-squared score, R2 score): 0.187243620959343
# generate irreducible fraction with an odd number as the denominator
# such numbers can work as the exponent for negative numbers and
# will be used as the parameter "C" in Power-law regression below:
# y = A * (B+b1*x1+b2*x2+...+bN*xN)**C + D
def gcd(a, b): # calculate the greatest common divisor of two numbers
while b:
a, b = b, a % b
return a
def generate_irreducible_fraction(existing_fractions = []):
while True:
numerator = random.randint(1, 400) # Random numerator
denominator = random.randrange(1, 100, 2) # Random odd denominator
if gcd(numerator, denominator) == 1: # Check if the fraction is irreducible
fraction = (numerator, denominator)
if fraction not in existing_fractions: # Check if the fraction is not a duplicate
return fraction
# Generate irreducible fraction numbers
N_faction = 40
upper_bound = 50
irreducible_fractions = []
while len(irreducible_fractions) < N_faction:
fraction = generate_irreducible_fraction(irreducible_fractions)
if fraction[0]/fraction[1] < upper_bound:
irreducible_fractions.append(fraction)
# Sort the irreducible fractions
irreducible_fractions.sort(key=lambda f: f[0] / f[1])
# Print the irreducible fraction numbers
for numerator, denominator in irreducible_fractions:
if random.random() <= 0.1:
print(f"{numerator}/{denominator}")
# Extract the numerator and denominator values
indexes = range(1, len(irreducible_fractions) + 1)
values = [numerator / denominator for numerator, denominator in irreducible_fractions]
# Plot the irreducible fractions
plt.plot(values, 'o-')
plt.xlabel("Index")
plt.ylabel("Irreducible Fraction")
plt.title("Irreducible Fractions")
plt.show()
## if not use the above random generated irreducible_fractions, define it below.
irreducible_fractions = [(1,95), (30,43), (179,65), (5,1), (221,33), (219,23), (300,17), (73,3)]
115/73 225/97 233/35
# # old code! The new one is in the next chunk.
# params_list = []
# for numerator, denominator in irreducible_fractions:
# C1, C2 = numerator, denominator
# # Define the model function
# def func(X, *params):
# A, B, D = params[:3]
# # Compute the weighted sum
# weighted_sum = np.sum(X * np.array(params[3:]), axis=1)
# base = weighted_sum + B
# abs_base = np.abs(base)
# sign = np.sign(base)
# power_result = np.power(abs_base, C1 / C2)
# return A * sign * power_result + D
# # Create a LinearRegression object
# model = linear_model.LinearRegression()
# # give the initial params using linear regression
# # so that the params are within a reasonable range
# model.fit(x_train, y_train)
# # print("Fitted Coefficients:", model.coef_)
# # print("Fitted Intercept:", model.intercept_)
# num_features = x_train.shape[1]
# initial_params = [1, model.intercept_, 0] + list(model.coef_) # Initial parameter guesses
# # Perform the curve fit
# params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# params_list.append(params)
# # Print the fitted parameters
# # print("Fitted Parameters:", params)
# # predict on test
# y_predict_test_list = []
# for (numerator, denominator), params in zip(irreducible_fractions, params_list):
# C1, C2 = numerator, denominator
# A, B, D = params[:3]
# weighted_sum = np.sum(x_test * np.array(params[3:]), axis=1)
# base = weighted_sum + B
# abs_base = np.abs(base)
# sign = np.sign(base)
# power_result = np.power(abs_base, C1 / C2)
# y_pred = A * sign * power_result + D
# y_predict_test_list.append(y_pred)
# # predict on train
# y_predict_train_list = []
# for (numerator, denominator), params in zip(irreducible_fractions, params_list):
# C1, C2 = numerator, denominator
# A, B, D = params[:3]
# weighted_sum = np.sum(x_train * np.array(params[3:]), axis=1)
# base = weighted_sum + B
# abs_base = np.abs(base)
# sign = np.sign(base)
# power_result = np.power(abs_base, C1 / C2)
# y_pred_ = A * sign * power_result + D
# y_predict_train_list.append(y_pred_)
# new code, a updated version for the code in last chunk.
# input and output data normalization is achieved (but it
# seems normalization is redundant).
class CurveFit_with_Normalization:
def __init__(self, exponent_numerator=1, exponent_denominator=1, input_range=[1,2], output_range=[1,2]):
self.input_min = input_range[0]
self.input_max = input_range[1]
self.output_min = output_range[0]
self.output_max = output_range[1]
self.input_scale = None
self.input_shift = None
self.output_scale = None
self.output_shift = None
self.exponent_numerator = exponent_numerator
self.exponent_denominator = exponent_denominator
self.linear_model = linear_model.LinearRegression()
def fit(self, X, y):
# Normalize the input and output data
self.input_scale = (self.input_max - self.input_min) / (np.max(X) - np.min(X))
self.input_shift = self.input_min - np.min(X) * self.input_scale
normalized_X = self.input_scale * X + self.input_shift
self.output_scale = (self.output_max - self.output_min) / (np.max(y) - np.min(y))
self.output_shift = self.output_min - np.min(y) * self.output_scale
normalized_y = self.output_scale * y + self.output_shift
def normalized_func_(X_normalize, *params):
A, B, D = params[:3]
# Compute the weighted sum
weighted_sum = np.sum(X_normalize * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, self.exponent_numerator / self.exponent_denominator)
return A * sign * power_result + D
# Give the initial params using linear regression
self.linear_model.fit(normalized_X, normalized_y)
# print("Fitted Coefficients:", linear_model.coef_)
# print("Fitted Intercept:", linear_model.intercept_)
# num_features = X.shape[1]
exponent = self.exponent_numerator / self.exponent_denominator
initial_params = [1, self.linear_model.intercept_ / exponent + (1 - 1 / exponent), 0] + list(self.linear_model.coef_ /
exponent) # Initial parameter guesses
# initial_params = [1, 0, 0] + [1 / X.shape[1]] * (X.shape[1])
# Perform the normalized curve fit
normalized_params, params_covariance = curve_fit(normalized_func_, normalized_X, normalized_y,
p0=initial_params, maxfev=100000000)
# Store the fitted parameters
self.normalized_fitted_params = normalized_params
def predict(self, X):
# Normalize the input data using the previously calculated scaling and shifting parameters
normalized_X = self.input_scale * X + self.input_shift
# Make predictions using the denormalized parameters
y_pred = self.normalized_func(normalized_X, self.exponent_numerator,
self.exponent_denominator, *self.normalized_fitted_params)
# Denormalize the predicted output
y_pred = (y_pred - self.output_shift) / self.output_scale
return y_pred
@staticmethod
def normalized_func(X_normalize, exponent_numerator, exponent_denominator, *params):
A, B, D = params[:3]
# Compute the weighted sum
weighted_sum = np.sum(X_normalize * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, exponent_numerator / exponent_denominator)
return A * sign * power_result + D
model_list = []
for numerator, denominator in irreducible_fractions:
# Create an instance of NormalizedCurveFit
model = CurveFit_with_Normalization(numerator, denominator, input_range=[1, 2], output_range=[1, 2])
# Fit the model to your input and output data
model.fit(x_train, y_train)
model_list.append(model)
# this is for the new version code in the last chunk
r2_score_test_list = []
# predict on test
y_predict_test_list = []
for model, (numerator, denominator) in zip(model_list, irreducible_fractions):
y_pred = model.predict(x_test)
print(f'-------- \n (numerator, denominator) is: ({numerator}, {denominator})')
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
r2_score_test_list.append(r_squared)
y_predict_test_list.append(y_pred)
print("|||||||||||||||||||||||||||||||||||||")
r2_score_train_list = []
# predict on train
y_predict_train_list = []
for model, (numerator, denominator) in zip(model_list, irreducible_fractions):
y_pred_ = model.predict(x_train)
print(f'-------- \n (numerator, denominator) is: ({numerator}, {denominator})')
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
r2_score_train_list.append(r_squared)
y_predict_train_list.append(y_pred_)
x = [numerator / denominator for (numerator, denominator) in irreducible_fractions]
# plot the r2 score curve over exponent
fig, ax = plt.subplots(figsize=(7.5, 5)) # Adjust the values as desired
# Plot the R-squared scores
ax.plot(x, r2_score_train_list, label='Train R-squared')
ax.plot(x, r2_score_test_list, label='Test R-squared')
# Set labels and title with font size
ax.set_xlabel('Exponent in Power Law', fontsize=14)
ax.set_ylabel('R-squared', fontsize=14)
ax.set_title('R-squared Scores', fontsize=16)
# Set tick label font size
ax.tick_params(axis='x', labelsize=12)
ax.tick_params(axis='y', labelsize=12)
# Set legend
ax.legend(fontsize=12)
fig.savefig('Power_Law_r2_scores_plot.png')
# Display the plot
plt.show()
-------- (numerator, denominator) is: (1, 95) Mean squared error: 0.001933283143492199 Correlation coefficient: 0.6021425216341963 Coefficient of determination (R-squared score, R2 score): 0.35978626282431625 -------- (numerator, denominator) is: (30, 43) Mean squared error: 0.0019349673229873147 Correlation coefficient: 0.6014597690280606 Coefficient of determination (R-squared score, R2 score): 0.35922854066537 -------- (numerator, denominator) is: (179, 65) Mean squared error: 0.002094368391858342 Correlation coefficient: 0.55806049241315 Coefficient of determination (R-squared score, R2 score): 0.3064422975559521 -------- (numerator, denominator) is: (5, 1) Mean squared error: 0.0021149947453885745 Correlation coefficient: 0.5536322377699431 Coefficient of determination (R-squared score, R2 score): 0.2996118056425723 -------- (numerator, denominator) is: (221, 33) Mean squared error: 0.0021206940775998205 Correlation coefficient: 0.5524436522501386 Coefficient of determination (R-squared score, R2 score): 0.2977244510734032 -------- (numerator, denominator) is: (219, 23) Mean squared error: 0.0021253505815068715 Correlation coefficient: 0.5514823060429244 Coefficient of determination (R-squared score, R2 score): 0.29618243288608204 -------- (numerator, denominator) is: (300, 17) Mean squared error: 0.002130220241811523 Correlation coefficient: 0.5504845391600146 Coefficient of determination (R-squared score, R2 score): 0.2945698271832332 -------- (numerator, denominator) is: (73, 3) Mean squared error: 0.0021317416709548567 Correlation coefficient: 0.5501763827654457 Coefficient of determination (R-squared score, R2 score): 0.2940660003946014 ||||||||||||||||||||||||||||||||||||| -------- (numerator, denominator) is: (1, 95) Mean squared error: 0.0014321085415216173 Correlation coefficient: 0.6015855539461997 Coefficient of determination (R-squared score, R2 score): 0.36190499068364634 -------- (numerator, denominator) is: (30, 43) Mean squared error: 0.0014311869137603856 Correlation coefficient: 0.6019266059696391 Coefficient of determination (R-squared score, R2 score): 0.3623156341913406 -------- (numerator, denominator) is: (179, 65) Mean squared error: 0.0014061586972142445 Correlation coefficient: 0.6111197019344603 Coefficient of determination (R-squared score, R2 score): 0.3734672889766777 -------- (numerator, denominator) is: (5, 1) Mean squared error: 0.0014046096107432882 Correlation coefficient: 0.6116841593579128 Coefficient of determination (R-squared score, R2 score): 0.3741575050583906 -------- (numerator, denominator) is: (221, 33) Mean squared error: 0.0014042222557862144 Correlation coefficient: 0.6118252173236781 Coefficient of determination (R-squared score, R2 score): 0.37433009621176805 -------- (numerator, denominator) is: (219, 23) Mean squared error: 0.001403911142670685 Correlation coefficient: 0.6119384910318577 Coefficient of determination (R-squared score, R2 score): 0.37446871679854354 -------- (numerator, denominator) is: (300, 17) Mean squared error: 0.001403597030136611 Correlation coefficient: 0.6120528371556796 Coefficient of determination (R-squared score, R2 score): 0.3746086738161475 -------- (numerator, denominator) is: (73, 3) Mean squared error: 0.0014035010091686935 Correlation coefficient: 0.6120877855637247 Coefficient of determination (R-squared score, R2 score): 0.3746514572355891
# for model in model_list:
# print(model.exponent_numerator, model.exponent_denominator)
# both the old and new versions (in the last subsection "Fit and predict") of code
# share the same evaluate code in this subsectoon.
# Create and update multiple figures (test)
for y_pred, (numerator, denominator) in zip(y_predict_test_list, irreducible_fractions):
plot_comparison(y_test, y_pred, f'Power-Law Regression Exponent={numerator} over {denominator}, Test Set')
# here pay attention: cannot use / replace over in the name, otherwise cannot save the fig
# because / cannot be in a file name.
print(y_pred[0])
clear_output(wait=True) # Clear the previous output
-0.0034288996429232
# Create and update multiple figures (train)
for y_pred_, (numerator, denominator) in zip(y_predict_train_list, irreducible_fractions):
plot_comparison(y_train, y_pred_, f'Power-Law Regression Exponent={numerator} over {denominator}, Train Set')
print(y_pred_[0])
clear_output(wait=True) # Clear the previous output
0.007488538817954552
Let $B = (b_1, b_2, \ldots , b_N)$. $$ y = A \cdot e^{(b_1 \cdot x_1 + \ldots + b_N \cdot x_N)} + C $$
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
x_train shape: (1368, 14) y_train shape: (1368,) x_test shape: (72, 14) y_test shape: (72,)
# Define the model function
def func(X, *params):
A, C = params[:2]
return A * np.exp(np.sum(X * np.array(params[2:]), axis=1)) + C
# give the initial params using linear regression
# so that the params are within a reasonable range
num_features = x_train.shape[1]
initial_params = [np.mean(y_train), 0] + [0] * num_features # Initial parameter guesses
# Perform the curve fit
params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# Print the fitted parameters
print("Fitted Parameters:", params)
# predict on test
A, C = params[:2]
y_pred = A * np.exp(np.sum(x_test * np.array(params[2:]), axis=1)) + C
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
# predict on train
A, C = params[:2]
y_pred_ = A * np.exp(np.sum(x_train * np.array(params[2:]), axis=1)) + C
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
r2_score_train_list.append(r_squared)
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
print(y_pred)
print(y_pred_test_digital)
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Fitted Parameters: [ 0.1231451 -0.10520813 1.40826714 0.17547963 -0.05617049 0.06929655 0.40501096 0.11387686 0.59424565 -0.10835117 1.07134255 -0.25469261 -2.97378161 -0.04621807 0.01919921 0.93342524] Mean squared error: 0.0021358732783242265 Correlation coefficient: 0.5493376423946233 Coefficient of determination (R-squared score, R2 score): 0.29269780360284303 Mean squared error: 0.0014032585370487949 Correlation coefficient: 0.6121760318027599 Coefficient of determination (R-squared score, R2 score): 0.37475949391375973 ---- ---- ---- [-0.00334645 -0.00376563 0.0160857 0.0127042 0.01246067 0.03020036 0.02106777 0.04228009 0.00669212 0.01582696 0.00589754 0.02738642 0.10935512 0.03017949 0.01930066 0.01370376 0.02346596 -0.00584292 0.02715794 -0.0164255 0.03967245 0.01107316 0.01753134 0.0040122 0.01261146 0.25587977 0.0183818 0.00910601 0.01889986 -0.00634774 0.01761428 0.02734232 -0.01057383 0.0069221 0.01866984 0.0022946 0.01199734 0.03020133 0.00341021 0.00573255 0.00345822 -0.00250562 0.03531443 0.02351427 0.01585078 0.03374845 0.00198065 0.01663137 0.00353382 0.13216855 0.01551792 0.03753382 0.02040369 0.01286201 0.01107566 -0.00323279 0.0067469 0.00245688 0.02033133 0.01342355 0.02449959 0.0210649 0.00631196 -0.00571621 -0.00038629 0.00863199 0.00660207 0.0042756 -0.00031217 0.01568242 0.01889709 0.03616918] [ 5 5 5 5 5 5 5 6 5 5 5 5 7 5 5 5 5 4 5 4 6 5 5 5 5 11 5 5 5 4 5 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 5 6 5 5 5 5 5 5 5 5 5 5 5 4 5 5 5 5 5 5 5 6] Mean squared error: 1.4305555555555556 Correlation coefficient: 0.5025479155614934 Coefficient of determination (R-squared score, R2 score): 0.23062558356676 Mean squared error: 0.966374269005848 Correlation coefficient: 0.5706022632062453 Coefficient of determination (R-squared score, R2 score): 0.32227663091482184
plot_comparison(y_test, y_pred, 'Exponential Regression, Test Set')
plot_comparison(y_train, y_pred_, 'Exponential Regression, Train Set')
# independent data
x = group_satcked_green
class_num = 480
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# print(np.max(y), np.min(y))
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
# print(intervals)
# Digitize the array to get the indices of the intervals
y_train = np.digitize(y_train, intervals) - 1
y_test = np.digitize(y_test, intervals) - 1
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
# to see unique elements (see if we have all 0, 1,..., class_num-1 classes, better close to all)
unique_elements = np.unique(y_train)
print("Unique elements:", unique_elements)
print("Number of unique elements:", len(unique_elements))
x_train shape: (1368, 14) y_train shape: (1368,) x_test shape: (72, 14) y_test shape: (72,) Unique elements: [ 65 71 72 75 79 80 85 88 91 94 95 99 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 244 245 248 250 252 255 256 257 259 260 262 265 268 269 270 274 278 297 304 335 341 346 350 353 357 378 429 479] Number of unique elements: 180
'multinomial' (default option for multi-calss) achieves better performance than 'ovr'.
# fit
model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, multi_class='multinomial')
# model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, multi_class='ovr')
fit_result = model.fit(x_train, y_train)
print(fit_result.intercept_.shape, fit_result.coef_.shape)
print("Coefficients:", model.coef_[0,:])
print("Intercept:", model.intercept_[0])
print('--- --- ---')
# predict
# Use the trained model to make predictions
y_pred = model.predict(x_test)
# Alternatively, you can get the predicted probabilities for each class
y_prob = model.predict_proba(x_test)
print('y_prob.shape:', y_prob.shape)
print(np.sum(y_prob, axis = 1))
print(y_prob[0,:])
# Print the predicted class labels
print('y_pred:', y_pred)
print('y_test:', y_test)
print('y_pred shape:', y_pred.shape, 'y_test shape:', y_test.shape)
# Print the predicted probabilities
# print(y_prob)
(180,) (180, 14) Coefficients: [ 4.43680280e-02 -7.55510583e-01 -1.93072516e-02 -2.76094341e-01 -2.08512610e-01 -9.01074611e-02 4.24861746e-02 1.20366864e-01 2.62561830e-02 3.60771444e-04 5.77757233e-02 8.65279651e-01 -7.96485984e-01 2.98289464e-02] Intercept: -5.4138964247043955 --- --- --- y_prob.shape: (72, 180) [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1.17412811e-05 5.56279889e-04 1.82831629e-03 2.07374948e-03 4.17092539e-04 1.68092643e-03 1.37897011e-03 5.13861379e-04 7.97788741e-04 1.81622565e-03 4.13082691e-04 4.47270129e-05 6.41850578e-04 6.00463831e-03 1.53739569e-03 1.79432550e-03 6.58739478e-03 1.22450615e-03 2.63219695e-04 4.94282540e-03 2.71103572e-03 2.36465338e-04 3.58918403e-03 2.64174438e-03 1.68242547e-03 6.24920069e-03 4.95190281e-03 4.82077291e-03 2.96339183e-03 1.31487630e-03 2.00533477e-04 6.31017288e-03 6.28105190e-04 5.27468546e-03 1.17097230e-02 2.61265958e-03 1.00537263e-02 8.75079207e-03 5.98106018e-03 6.61618596e-03 1.34045469e-02 1.90258050e-03 8.97383066e-03 7.80368127e-03 1.10079708e-02 2.10948480e-02 1.29083869e-02 8.15884841e-03 1.21813200e-02 1.11664494e-02 4.78637600e-03 2.34367987e-02 2.39643902e-02 2.02294883e-02 1.67281324e-02 2.25360449e-02 1.66173607e-02 1.42029800e-02 2.27173749e-02 1.54606841e-02 1.85442996e-02 2.26195628e-02 1.03233450e-02 1.74284071e-02 6.44200072e-03 1.36817849e-02 1.61147512e-02 1.28622911e-02 2.35690177e-02 2.42871326e-02 1.74390525e-02 1.16474530e-02 5.14531991e-03 2.86143970e-02 9.75394234e-03 1.24133700e-02 1.21314297e-02 1.17006510e-02 2.03950446e-02 1.37385215e-02 1.43387968e-02 1.16634687e-02 1.92936703e-02 9.54883053e-03 1.51022479e-02 1.13257412e-02 9.92622076e-03 6.35749825e-03 1.75825877e-02 6.39169844e-03 5.32239862e-03 3.79138923e-03 7.27055143e-03 7.91983669e-03 4.56904114e-03 6.07558899e-03 1.06399892e-02 5.25240727e-03 5.67394724e-03 4.10683944e-03 4.47762707e-03 1.10620010e-02 2.23732455e-03 5.54372289e-03 1.05246185e-02 3.55049519e-03 3.53704554e-03 5.64989536e-03 1.99913996e-03 1.79966064e-03 1.44913365e-03 2.25092824e-03 2.31901353e-03 2.45628641e-03 1.18821511e-03 5.37117659e-03 6.86612418e-04 1.64821818e-03 2.25189001e-03 1.52451501e-03 2.20869831e-03 1.46198824e-04 1.28506212e-03 2.37128983e-03 9.32007133e-04 1.13937514e-03 7.85558263e-06 6.22551572e-04 9.18398969e-04 2.84359101e-04 1.93741394e-03 1.54740007e-04 8.31903165e-04 1.88408016e-04 5.87310751e-04 8.43896491e-04 1.06466301e-03 3.28760004e-06 1.41819834e-03 2.22514420e-04 4.45019505e-04 5.14067269e-04 2.80962356e-04 3.06802220e-04 3.28221890e-04 4.16681844e-06 1.34310973e-07 3.16626255e-05 4.34330948e-05 7.85673934e-05 3.60189079e-04 7.02322537e-04 6.59995288e-04 4.40038343e-11 7.76705694e-05 1.87965132e-04 1.57391369e-04 7.95634815e-06 1.36666145e-03 1.55479629e-04 1.13920222e-05 1.30305154e-07 4.05718706e-04 1.52757265e-04 2.87216663e-04 2.39027381e-06 3.98909108e-04 1.17934699e-10 3.67693376e-05 1.58566131e-04 4.42882447e-06 9.42133877e-07 1.34125005e-07 3.83722768e-16 1.61785478e-05 1.59852575e-06 3.26116040e-07 1.19345251e-08 3.32422375e-07 3.69800480e-06] y_pred: [162 141 167 152 170 169 168 166 162 170 158 167 260 138 162 170 157 143 162 99 189 152 167 186 162 378 152 190 140 162 162 166 162 162 190 140 154 180 163 170 158 147 166 162 163 167 152 138 170 202 153 166 190 166 174 158 167 162 190 170 162 162 190 140 134 163 158 152 162 158 199 184] y_test: [153 188 169 125 156 138 190 188 168 182 167 158 261 179 183 152 126 170 256 0 170 174 159 138 146 263 183 164 139 139 161 172 145 151 135 122 141 181 173 166 188 125 172 307 193 155 156 180 151 275 143 177 172 162 178 156 153 148 165 177 219 146 169 175 157 190 136 79 202 170 163 181] y_pred shape: (72,) y_test shape: (72,)
In previous data division, I classify data into class_num (e.g., class_num = 160) intervals (histogram, by np.digitize). Here, evaluate the results with the same number of classes (e.g., class_num = 160).
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)
cm = confusion_matrix(y_test, y_pred)
print("Confusion Matrix:") # y_test doesn't include all classes, so confusion matrix is less than num_class by num_class
print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
# Sort y_pred and y_test based on y_test
plot_comparison(y_test, y_pred, 'Logistic Linear Regression, Test Set')
Accuracy: 0.0 Confusion Matrix: [[0 0 1 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] ... [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0]] Mean squared error: 1376.4444444444443 Correlation coefficient: 0.4994740362981341 Coefficient of determination (R-squared score, R2 score): 0.16921003739870966
# predict on train
# Use the trained model to make predictions
y_pred_ = model.predict(x_train)
# Alternatively, you can get the predicted probabilities for each class
y_prob_ = model.predict_proba(x_train)
accuracy = accuracy_score(y_train, y_pred_)
print("Accuracy:", accuracy)
cm = confusion_matrix(y_train, y_pred_)
print("Confusion Matrix:")
print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Logistic Linear Regression, Train Set')
Accuracy: 0.056286549707602336 Confusion Matrix: [[1 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] ... [0 0 0 ... 1 0 0] [0 0 0 ... 0 1 0] [0 0 0 ... 0 0 1]] Mean squared error: 1027.3567251461989 Correlation coefficient: 0.5033106063931366 Coefficient of determination (R-squared score, R2 score): 0.16605880363558412
The model is based on classifying data into class_num (e.g., class_num = 160) intervals (histogram, by np.digitize). Here, evaluate the results a smaller number of classes (e.g., reduced_class_num = 16), that is, for the example of class_num = 160 and reduced_class_num = 16, classes 0, 1, ..., 15 become one class, i.e., 0; ...; classes 144, 145, ..., 159 become one class, i.e., 15.
print("---- ---- ----")
# Define the boundaries for digitization
reduced_class_num = 16
intervals = np.arange(0, class_num + 1, class_num / reduced_class_num)
print(intervals)
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
print(y_pred)
print(y_pred_test_digital)
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- [ 0. 30. 60. 90. 120. 150. 180. 210. 240. 270. 300. 330. 360. 390. 420. 450. 480.] [162 141 167 152 170 169 168 166 162 170 158 167 260 138 162 170 157 143 162 99 189 152 167 186 162 378 152 190 140 162 162 166 162 162 190 140 154 180 163 170 158 147 166 162 163 167 152 138 170 202 153 166 190 166 174 158 167 162 190 170 162 162 190 140 134 163 158 152 162 158 199 184] [ 5 4 5 5 5 5 5 5 5 5 5 5 8 4 5 5 5 4 5 3 6 5 5 6 5 12 5 6 4 5 5 5 5 5 6 4 5 6 5 5 5 4 5 5 5 5 5 4 5 6 5 5 6 5 5 5 5 5 6 5 5 5 6 4 4 5 5 5 5 5 6 6] Mean squared error: 1.7638888888888888 Correlation coefficient: 0.4211442366633511 Coefficient of determination (R-squared score, R2 score): 0.05135387488328669 Mean squared error: 1.266812865497076 Correlation coefficient: 0.46808281720782485 Coefficient of determination (R-squared score, R2 score): 0.11157745943675201
Fixing the reduced class number, I enumerate the original class number to see what a original class number is better.
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
reduced_class_num = 16
class_num_array = np.arange(reduced_class_num, reduced_class_num * 100 + 1, reduced_class_num)
mse_test_list = []
correlation_test_list = []
r_squared_test_list = []
mse_train_list = []
correlation_train_list = []
r_squared_train_list = []
for class_num in class_num_array:
print('---- ---- ----')
print(f'class_num = {class_num}')
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
# print(intervals)
# Digitize the array to get the indices of the intervals
y_train = np.digitize(y_train, intervals) - 1
y_test = np.digitize(y_test, intervals) - 1
# to see unique elements (see if we have all 0, 1,..., class_num-1 classes, better close to all)
unique_elements = np.unique(y_train)
# print("Unique elements:", unique_elements)
print("Number of unique elements:", len(unique_elements))
model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, multi_class='multinomial')
fit_result = model.fit(x_train, y_train)
y_pred = model.predict(x_test)
y_pred_ = model.predict(x_train)
# Define the boundaries for digitization
intervals = np.arange(0, class_num+1, class_num/16)
print(intervals)
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
# print(y_pred)
# print(y_pred_test_digital)
print("test eval:")
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse_test_list.append(mse)
correlation_test_list.append(correlation)
r_squared_test_list.append(r_squared)
print("train eval:")
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse_train_list.append(mse)
correlation_train_list.append(correlation)
r_squared_train_list.append(r_squared)
plot_comparison(y_test, y_pred, f'Logistic Linear Regression Reduced Evaluation {class_num} to {reduced_class_num}, Test Set')
plot_comparison(y_train, y_pred_, f'Logistic Linear Regression Reduced Evaluation {class_num} to {reduced_class_num}, Train Set')
x_train shape: (1368, 14) y_train shape: (1368,) x_test shape: (72, 14) y_test shape: (72,) ---- ---- ---- class_num = 16 Number of unique elements: 13 [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.] test eval: Mean squared error: 1.5694444444444444 Correlation coefficient: 0.4313763983222873 Coefficient of determination (R-squared score, R2 score): 0.15592903828197946 train eval: Mean squared error: 1.090643274853801 Correlation coefficient: 0.4937423525584534 Coefficient of determination (R-squared score, R2 score): 0.23512612203094863
---- ---- ---- class_num = 32 Number of unique elements: 22 [ 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. 22. 24. 26. 28. 30. 32.] test eval: Mean squared error: 1.6944444444444444 Correlation coefficient: 0.4584227078059493 Coefficient of determination (R-squared score, R2 score): 0.08870214752567696 train eval: Mean squared error: 1.1366959064327486 Correlation coefficient: 0.47776357570271016 Coefficient of determination (R-squared score, R2 score): 0.20282916873868984
---- ---- ---- class_num = 48 Number of unique elements: 30 [ 0. 3. 6. 9. 12. 15. 18. 21. 24. 27. 30. 33. 36. 39. 42. 45. 48.] test eval: Mean squared error: 1.8611111111111112 Correlation coefficient: 0.44599985139572335 Coefficient of determination (R-squared score, R2 score): -0.0009337068160597539 train eval: Mean squared error: 1.128654970760234 Correlation coefficient: 0.5022382379453247 Coefficient of determination (R-squared score, R2 score): 0.2084683193135286
---- ---- ---- class_num = 64 Number of unique elements: 39 [ 0. 4. 8. 12. 16. 20. 24. 28. 32. 36. 40. 44. 48. 52. 56. 60. 64.] test eval: Mean squared error: 1.4583333333333333 Correlation coefficient: 0.4840479486774242 Coefficient of determination (R-squared score, R2 score): 0.21568627450980393 train eval: Mean squared error: 1.1776315789473684 Correlation coefficient: 0.45338293644373096 Coefficient of determination (R-squared score, R2 score): 0.17412076581223745
---- ---- ---- class_num = 80 Number of unique elements: 47 [ 0. 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. 55. 60. 65. 70. 75. 80.] test eval: Mean squared error: 1.6944444444444444 Correlation coefficient: 0.4379020436734468 Coefficient of determination (R-squared score, R2 score): 0.08870214752567696 train eval: Mean squared error: 1.1374269005847952 Correlation coefficient: 0.49018613302448594 Coefficient of determination (R-squared score, R2 score): 0.20231651868643175
---- ---- ---- class_num = 96 Number of unique elements: 53 [ 0. 6. 12. 18. 24. 30. 36. 42. 48. 54. 60. 66. 72. 78. 84. 90. 96.] test eval: Mean squared error: 1.7222222222222223 Correlation coefficient: 0.4322037575423 Coefficient of determination (R-squared score, R2 score): 0.07376283846872078 train eval: Mean squared error: 1.1951754385964912 Correlation coefficient: 0.4696957812482653 Coefficient of determination (R-squared score, R2 score): 0.16181716455804362
---- ---- ---- class_num = 112 Number of unique elements: 61 [ 0. 7. 14. 21. 28. 35. 42. 49. 56. 63. 70. 77. 84. 91. 98. 105. 112.] test eval: Mean squared error: 1.4027777777777777 Correlation coefficient: 0.5256920691801376 Coefficient of determination (R-squared score, R2 score): 0.24556489262371617 train eval: Mean squared error: 1.1432748538011697 Correlation coefficient: 0.4774943818557002 Coefficient of determination (R-squared score, R2 score): 0.19821531826836714
---- ---- ---- class_num = 128 Number of unique elements: 68 [ 0. 8. 16. 24. 32. 40. 48. 56. 64. 72. 80. 88. 96. 104. 112. 120. 128.] test eval: Mean squared error: 1.3333333333333333 Correlation coefficient: 0.556725805264799 Coefficient of determination (R-squared score, R2 score): 0.28291316526610644 train eval: Mean squared error: 1.168859649122807 Correlation coefficient: 0.49186512535553734 Coefficient of determination (R-squared score, R2 score): 0.18027256643933443
---- ---- ---- class_num = 144 Number of unique elements: 75 [ 0. 9. 18. 27. 36. 45. 54. 63. 72. 81. 90. 99. 108. 117. 126. 135. 144.] test eval: Mean squared error: 1.5416666666666667 Correlation coefficient: 0.49476274731670417 Coefficient of determination (R-squared score, R2 score): 0.17086834733893552 train eval: Mean squared error: 1.154970760233918 Correlation coefficient: 0.5074756435679069 Coefficient of determination (R-squared score, R2 score): 0.19001291743223792
---- ---- ---- class_num = 160 Number of unique elements: 80 [ 0. 10. 20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 120. 130. 140. 150. 160.] test eval: Mean squared error: 1.4583333333333333 Correlation coefficient: 0.4840479486774242 Coefficient of determination (R-squared score, R2 score): 0.21568627450980393 train eval: Mean squared error: 1.1586257309941521 Correlation coefficient: 0.4876647688470753 Coefficient of determination (R-squared score, R2 score): 0.18744966717094746
---- ---- ---- class_num = 176 Number of unique elements: 85 [ 0. 11. 22. 33. 44. 55. 66. 77. 88. 99. 110. 121. 132. 143. 154. 165. 176.] test eval: Mean squared error: 1.3194444444444444 Correlation coefficient: 0.5549898271829921 Coefficient of determination (R-squared score, R2 score): 0.29038281979458447 train eval: Mean squared error: 1.1915204678362572 Correlation coefficient: 0.489140711054498 Coefficient of determination (R-squared score, R2 score): 0.16438041481933396
---- ---- ---- class_num = 192 Number of unique elements: 93 [ 0. 12. 24. 36. 48. 60. 72. 84. 96. 108. 120. 132. 144. 156. 168. 180. 192.] test eval: Mean squared error: 1.5555555555555556 Correlation coefficient: 0.4947426083580659 Coefficient of determination (R-squared score, R2 score): 0.1633986928104575 train eval: Mean squared error: 1.1432748538011697 Correlation coefficient: 0.5057620567304648 Coefficient of determination (R-squared score, R2 score): 0.19821531826836714
---- ---- ---- class_num = 208 Number of unique elements: 96 [ 0. 13. 26. 39. 52. 65. 78. 91. 104. 117. 130. 143. 156. 169. 182. 195. 208.] test eval: Mean squared error: 1.3472222222222223 Correlation coefficient: 0.5413682524632262 Coefficient of determination (R-squared score, R2 score): 0.2754435107376284 train eval: Mean squared error: 1.1600877192982457 Correlation coefficient: 0.4946974442669705 Coefficient of determination (R-squared score, R2 score): 0.18642436706643128
---- ---- ---- class_num = 224 Number of unique elements: 99 [ 0. 14. 28. 42. 56. 70. 84. 98. 112. 126. 140. 154. 168. 182. 196. 210. 224.] test eval: Mean squared error: 1.4305555555555556 Correlation coefficient: 0.4934320296098701 Coefficient of determination (R-squared score, R2 score): 0.23062558356676 train eval: Mean squared error: 1.1571637426900585 Correlation coefficient: 0.48157227111910395 Coefficient of determination (R-squared score, R2 score): 0.18847496727546365
---- ---- ---- class_num = 240 Number of unique elements: 107 [ 0. 15. 30. 45. 60. 75. 90. 105. 120. 135. 150. 165. 180. 195. 210. 225. 240.] test eval: Mean squared error: 1.5694444444444444 Correlation coefficient: 0.47278614818119935 Coefficient of determination (R-squared score, R2 score): 0.15592903828197946 train eval: Mean squared error: 1.1637426900584795 Correlation coefficient: 0.4906183882824831 Coefficient of determination (R-squared score, R2 score): 0.18386111680514095
---- ---- ---- class_num = 256 Number of unique elements: 112 [ 0. 16. 32. 48. 64. 80. 96. 112. 128. 144. 160. 176. 192. 208. 224. 240. 256.] test eval: Mean squared error: 1.6388888888888888 Correlation coefficient: 0.45650691560224516 Coefficient of determination (R-squared score, R2 score): 0.11858076563958919 train eval: Mean squared error: 1.1805555555555556 Correlation coefficient: 0.5002004759466409 Coefficient of determination (R-squared score, R2 score): 0.1720701656032052
---- ---- ---- class_num = 272 Number of unique elements: 118 [ 0. 17. 34. 51. 68. 85. 102. 119. 136. 153. 170. 187. 204. 221. 238. 255. 272.] test eval: Mean squared error: 1.375 Correlation coefficient: 0.519590699723782 Coefficient of determination (R-squared score, R2 score): 0.26050420168067223 train eval: Mean squared error: 1.266812865497076 Correlation coefficient: 0.4647542985426648 Coefficient of determination (R-squared score, R2 score): 0.11157745943675201
---- ---- ---- class_num = 288 Number of unique elements: 123 [ 0. 18. 36. 54. 72. 90. 108. 126. 144. 162. 180. 198. 216. 234. 252. 270. 288.] test eval: Mean squared error: 1.5694444444444444 Correlation coefficient: 0.4834781742074105 Coefficient of determination (R-squared score, R2 score): 0.15592903828197946 train eval: Mean squared error: 1.1461988304093567 Correlation coefficient: 0.51093149794372 Coefficient of determination (R-squared score, R2 score): 0.19616471805933478
---- ---- ---- class_num = 304 Number of unique elements: 128 [ 0. 19. 38. 57. 76. 95. 114. 133. 152. 171. 190. 209. 228. 247. 266. 285. 304.] test eval: Mean squared error: 1.6388888888888888 Correlation coefficient: 0.4617270814263192 Coefficient of determination (R-squared score, R2 score): 0.11858076563958919 train eval: Mean squared error: 1.2076023391812865 Correlation coefficient: 0.49387353995205285 Coefficient of determination (R-squared score, R2 score): 0.15310211366965631
---- ---- ---- class_num = 320 Number of unique elements: 131 [ 0. 20. 40. 60. 80. 100. 120. 140. 160. 180. 200. 220. 240. 260. 280. 300. 320.] test eval: Mean squared error: 1.4444444444444444 Correlation coefficient: 0.49474260835806494 Coefficient of determination (R-squared score, R2 score): 0.22315592903828196 train eval: Mean squared error: 1.236842105263158 Correlation coefficient: 0.46910805103925024 Coefficient of determination (R-squared score, R2 score): 0.13259611157933315
---- ---- ---- class_num = 336 Number of unique elements: 137 [ 0. 21. 42. 63. 84. 105. 126. 147. 168. 189. 210. 231. 252. 273. 294. 315. 336.] test eval: Mean squared error: 1.8055555555555556 Correlation coefficient: 0.41416566626650614 Coefficient of determination (R-squared score, R2 score): 0.028944911297852483 train eval: Mean squared error: 1.236842105263158 Correlation coefficient: 0.49002401933027445 Coefficient of determination (R-squared score, R2 score): 0.13259611157933315
---- ---- ---- class_num = 352 Number of unique elements: 142 [ 0. 22. 44. 66. 88. 110. 132. 154. 176. 198. 220. 242. 264. 286. 308. 330. 352.] test eval: Mean squared error: 1.6388888888888888 Correlation coefficient: 0.46938438711823416 Coefficient of determination (R-squared score, R2 score): 0.11858076563958919 train eval: Mean squared error: 1.2141812865497077 Correlation coefficient: 0.48797738693377524 Coefficient of determination (R-squared score, R2 score): 0.14848826319933361
---- ---- ---- class_num = 368 Number of unique elements: 145 [ 0. 23. 46. 69. 92. 115. 138. 161. 184. 207. 230. 253. 276. 299. 322. 345. 368.] test eval: Mean squared error: 1.5277777777777777 Correlation coefficient: 0.5151516856124113 Coefficient of determination (R-squared score, R2 score): 0.17833800186741366 train eval: Mean squared error: 1.2002923976608186 Correlation coefficient: 0.47276351140580186 Coefficient of determination (R-squared score, R2 score): 0.1582286141922371
---- ---- ---- class_num = 384 Number of unique elements: 154 [ 0. 24. 48. 72. 96. 120. 144. 168. 192. 216. 240. 264. 288. 312. 336. 360. 384.] test eval: Mean squared error: 1.7916666666666667 Correlation coefficient: 0.4330188277111793 Coefficient of determination (R-squared score, R2 score): 0.036414565826330514 train eval: Mean squared error: 1.213450292397661 Correlation coefficient: 0.4976300934411591 Coefficient of determination (R-squared score, R2 score): 0.1490009132515917
---- ---- ---- class_num = 400 Number of unique elements: 154 [ 0. 25. 50. 75. 100. 125. 150. 175. 200. 225. 250. 275. 300. 325. 350. 375. 400.] test eval: Mean squared error: 1.6805555555555556 Correlation coefficient: 0.4638039455832802 Coefficient of determination (R-squared score, R2 score): 0.09617180205415499 train eval: Mean squared error: 1.2375730994152048 Correlation coefficient: 0.4811788624464507 Coefficient of determination (R-squared score, R2 score): 0.13208346152707517
---- ---- ---- class_num = 416 Number of unique elements: 159 [ 0. 26. 52. 78. 104. 130. 156. 182. 208. 234. 260. 286. 312. 338. 364. 390. 416.] test eval: Mean squared error: 1.5833333333333333 Correlation coefficient: 0.47388885496854305 Coefficient of determination (R-squared score, R2 score): 0.14845938375350143 train eval: Mean squared error: 1.206140350877193 Correlation coefficient: 0.49221705881315964 Coefficient of determination (R-squared score, R2 score): 0.1541274137741725
---- ---- ---- class_num = 432 Number of unique elements: 165 [ 0. 27. 54. 81. 108. 135. 162. 189. 216. 243. 270. 297. 324. 351. 378. 405. 432.] test eval: Mean squared error: 1.6388888888888888 Correlation coefficient: 0.4673074723829523 Coefficient of determination (R-squared score, R2 score): 0.11858076563958919 train eval: Mean squared error: 1.2288011695906433 Correlation coefficient: 0.49090788967364374 Coefficient of determination (R-squared score, R2 score): 0.13823526215417203
---- ---- ---- class_num = 448 Number of unique elements: 170 [ 0. 28. 56. 84. 112. 140. 168. 196. 224. 252. 280. 308. 336. 364. 392. 420. 448.] test eval: Mean squared error: 1.6111111111111112 Correlation coefficient: 0.4714267300321648 Coefficient of determination (R-squared score, R2 score): 0.13352007469654525 train eval: Mean squared error: 1.2339181286549707 Correlation coefficient: 0.4766261895718343 Coefficient of determination (R-squared score, R2 score): 0.13464671178836551
---- ---- ---- class_num = 464 Number of unique elements: 173 [ 0. 29. 58. 87. 116. 145. 174. 203. 232. 261. 290. 319. 348. 377. 406. 435. 464.] test eval: Mean squared error: 1.625 Correlation coefficient: 0.47902818865469377 Coefficient of determination (R-squared score, R2 score): 0.12605042016806722 train eval: Mean squared error: 1.2273391812865497 Correlation coefficient: 0.4904867276327678 Coefficient of determination (R-squared score, R2 score): 0.13926056225868821
---- ---- ---- class_num = 480 Number of unique elements: 180 [ 0. 30. 60. 90. 120. 150. 180. 210. 240. 270. 300. 330. 360. 390. 420. 450. 480.] test eval: Mean squared error: 1.7638888888888888 Correlation coefficient: 0.4211442366633511 Coefficient of determination (R-squared score, R2 score): 0.05135387488328669 train eval: Mean squared error: 1.266812865497076 Correlation coefficient: 0.46808281720782485 Coefficient of determination (R-squared score, R2 score): 0.11157745943675201
---- ---- ---- class_num = 496 Number of unique elements: 183 [ 0. 31. 62. 93. 124. 155. 186. 217. 248. 279. 310. 341. 372. 403. 434. 465. 496.] test eval: Mean squared error: 1.625 Correlation coefficient: 0.46641526245836146 Coefficient of determination (R-squared score, R2 score): 0.12605042016806722 train eval: Mean squared error: 1.2251461988304093 Correlation coefficient: 0.4843054040900157 Coefficient of determination (R-squared score, R2 score): 0.14079851241546248
---- ---- ---- class_num = 512 Number of unique elements: 188 [ 0. 32. 64. 96. 128. 160. 192. 224. 256. 288. 320. 352. 384. 416. 448. 480. 512.] test eval: Mean squared error: 1.4861111111111112 Correlation coefficient: 0.5227266281332706 Coefficient of determination (R-squared score, R2 score): 0.20074696545284776 train eval: Mean squared error: 1.2339181286549707 Correlation coefficient: 0.48039431169055996 Coefficient of determination (R-squared score, R2 score): 0.13464671178836551
---- ---- ---- class_num = 528 Number of unique elements: 189 [ 0. 33. 66. 99. 132. 165. 198. 231. 264. 297. 330. 363. 396. 429. 462. 495. 528.] test eval: Mean squared error: 1.7083333333333333 Correlation coefficient: 0.4444117761914987 Coefficient of determination (R-squared score, R2 score): 0.08123249299719892 train eval: Mean squared error: 1.2646198830409356 Correlation coefficient: 0.4592505980608183 Coefficient of determination (R-squared score, R2 score): 0.11311540959352628
---- ---- ---- class_num = 544 Number of unique elements: 196 [ 0. 34. 68. 102. 136. 170. 204. 238. 272. 306. 340. 374. 408. 442. 476. 510. 544.] test eval: Mean squared error: 1.7361111111111112 Correlation coefficient: 0.45389174897251083 Coefficient of determination (R-squared score, R2 score): 0.06629318394024275 train eval: Mean squared error: 1.2711988304093567 Correlation coefficient: 0.4820927468692748 Coefficient of determination (R-squared score, R2 score): 0.10850155912320358
---- ---- ---- class_num = 560 Number of unique elements: 198 [ 0. 35. 70. 105. 140. 175. 210. 245. 280. 315. 350. 385. 420. 455. 490. 525. 560.] test eval: Mean squared error: 1.625 Correlation coefficient: 0.48431579273990755 Coefficient of determination (R-squared score, R2 score): 0.12605042016806722 train eval: Mean squared error: 1.284356725146199 Correlation coefficient: 0.46850961128253155 Coefficient of determination (R-squared score, R2 score): 0.09927385818255818
---- ---- ---- class_num = 576 Number of unique elements: 205 [ 0. 36. 72. 108. 144. 180. 216. 252. 288. 324. 360. 396. 432. 468. 504. 540. 576.] test eval: Mean squared error: 1.6388888888888888 Correlation coefficient: 0.4736868024382108 Coefficient of determination (R-squared score, R2 score): 0.11858076563958919 train eval: Mean squared error: 1.3011695906432748 Correlation coefficient: 0.47278752687944153 Coefficient of determination (R-squared score, R2 score): 0.08748290698062244
---- ---- ---- class_num = 592 Number of unique elements: 211 [ 0. 37. 74. 111. 148. 185. 222. 259. 296. 333. 370. 407. 444. 481. 518. 555. 592.] test eval: Mean squared error: 1.6944444444444444 Correlation coefficient: 0.45983338380168265 Coefficient of determination (R-squared score, R2 score): 0.08870214752567696 train eval: Mean squared error: 1.159356725146199 Correlation coefficient: 0.5111240982192807 Coefficient of determination (R-squared score, R2 score): 0.18693701711868937
---- ---- ---- class_num = 608 Number of unique elements: 216 [ 0. 38. 76. 114. 152. 190. 228. 266. 304. 342. 380. 418. 456. 494. 532. 570. 608.] test eval: Mean squared error: 1.7222222222222223 Correlation coefficient: 0.457272157858806 Coefficient of determination (R-squared score, R2 score): 0.07376283846872078 train eval: Mean squared error: 1.263157894736842 Correlation coefficient: 0.48105522590225747 Coefficient of determination (R-squared score, R2 score): 0.11414070969804246
---- ---- ---- class_num = 624 Number of unique elements: 216 [ 0. 39. 78. 117. 156. 195. 234. 273. 312. 351. 390. 429. 468. 507. 546. 585. 624.] test eval: Mean squared error: 1.7222222222222223 Correlation coefficient: 0.43217654821503354 Coefficient of determination (R-squared score, R2 score): 0.07376283846872078 train eval: Mean squared error: 1.222953216374269 Correlation coefficient: 0.48830408417944543 Coefficient of determination (R-squared score, R2 score): 0.14233646257223664
---- ---- ---- class_num = 640 Number of unique elements: 220 [ 0. 40. 80. 120. 160. 200. 240. 280. 320. 360. 400. 440. 480. 520. 560. 600. 640.] test eval: Mean squared error: 1.8888888888888888 Correlation coefficient: 0.39760029426461285 Coefficient of determination (R-squared score, R2 score): -0.015873015873015817 train eval: Mean squared error: 1.273391812865497 Correlation coefficient: 0.46698553728016656 Coefficient of determination (R-squared score, R2 score): 0.10696360896642931
---- ---- ---- class_num = 656 Number of unique elements: 223 [ 0. 41. 82. 123. 164. 205. 246. 287. 328. 369. 410. 451. 492. 533. 574. 615. 656.] test eval: Mean squared error: 1.6388888888888888 Correlation coefficient: 0.47067041449539393 Coefficient of determination (R-squared score, R2 score): 0.11858076563958919 train eval: Mean squared error: 1.2339181286549707 Correlation coefficient: 0.48668938380638976 Coefficient of determination (R-squared score, R2 score): 0.13464671178836551
---- ---- ---- class_num = 672 Number of unique elements: 227 [ 0. 42. 84. 126. 168. 210. 252. 294. 336. 378. 420. 462. 504. 546. 588. 630. 672.] test eval: Mean squared error: 1.6805555555555556 Correlation coefficient: 0.46085127853657204 Coefficient of determination (R-squared score, R2 score): 0.09617180205415499 train eval: Mean squared error: 1.202485380116959 Correlation coefficient: 0.5021835032786801 Coefficient of determination (R-squared score, R2 score): 0.15669066403546283
---- ---- ---- class_num = 688 Number of unique elements: 230 [ 0. 43. 86. 129. 172. 215. 258. 301. 344. 387. 430. 473. 516. 559. 602. 645. 688.] test eval: Mean squared error: 1.7916666666666667 Correlation coefficient: 0.4292277404851313 Coefficient of determination (R-squared score, R2 score): 0.036414565826330514 train eval: Mean squared error: 1.239766081871345 Correlation coefficient: 0.4870438032788566 Coefficient of determination (R-squared score, R2 score): 0.1305455113703009
---- ---- ---- class_num = 704 Number of unique elements: 239 [ 0. 44. 88. 132. 176. 220. 264. 308. 352. 396. 440. 484. 528. 572. 616. 660. 704.] test eval: Mean squared error: 1.8194444444444444 Correlation coefficient: 0.4015664186487819 Coefficient of determination (R-squared score, R2 score): 0.02147525676937445 train eval: Mean squared error: 1.1842105263157894 Correlation coefficient: 0.5091227863767976 Coefficient of determination (R-squared score, R2 score): 0.16950691534191475
---- ---- ---- class_num = 720 Number of unique elements: 240 [ 0. 45. 90. 135. 180. 225. 270. 315. 360. 405. 450. 495. 540. 585. 630. 675. 720.] test eval: Mean squared error: 1.8055555555555556 Correlation coefficient: 0.4078455240688131 Coefficient of determination (R-squared score, R2 score): 0.028944911297852483 train eval: Mean squared error: 1.3092105263157894 Correlation coefficient: 0.45743224601561033 Coefficient of determination (R-squared score, R2 score): 0.08184375640578356
---- ---- ---- class_num = 736 Number of unique elements: 241 [ 0. 46. 92. 138. 184. 230. 276. 322. 368. 414. 460. 506. 552. 598. 644. 690. 736.] test eval: Mean squared error: 1.5694444444444444 Correlation coefficient: 0.4879093790533349 Coefficient of determination (R-squared score, R2 score): 0.15592903828197946 train eval: Mean squared error: 1.2046783625730995 Correlation coefficient: 0.49265513537275685 Coefficient of determination (R-squared score, R2 score): 0.15515271387868856
---- ---- ---- class_num = 752 Number of unique elements: 249 [ 0. 47. 94. 141. 188. 235. 282. 329. 376. 423. 470. 517. 564. 611. 658. 705. 752.] test eval: Mean squared error: 1.5833333333333333 Correlation coefficient: 0.4779313399742912 Coefficient of determination (R-squared score, R2 score): 0.14845938375350143 train eval: Mean squared error: 1.2032163742690059 Correlation coefficient: 0.5106365275691869 Coefficient of determination (R-squared score, R2 score): 0.15617801398320474
---- ---- ---- class_num = 768 Number of unique elements: 255 [ 0. 48. 96. 144. 192. 240. 288. 336. 384. 432. 480. 528. 576. 624. 672. 720. 768.] test eval: Mean squared error: 1.8888888888888888 Correlation coefficient: 0.39529536502249907 Coefficient of determination (R-squared score, R2 score): -0.015873015873015817 train eval: Mean squared error: 1.2580409356725146 Correlation coefficient: 0.49092085211589764 Coefficient of determination (R-squared score, R2 score): 0.11772926006384898
---- ---- ---- class_num = 784 Number of unique elements: 254 [ 0. 49. 98. 147. 196. 245. 294. 343. 392. 441. 490. 539. 588. 637. 686. 735. 784.] test eval: Mean squared error: 1.7083333333333333 Correlation coefficient: 0.4514461504031727 Coefficient of determination (R-squared score, R2 score): 0.08123249299719892 train eval: Mean squared error: 1.1798245614035088 Correlation coefficient: 0.4986158100222583 Coefficient of determination (R-squared score, R2 score): 0.17258281565546318
---- ---- ---- class_num = 800 Number of unique elements: 254 [ 0. 50. 100. 150. 200. 250. 300. 350. 400. 450. 500. 550. 600. 650. 700. 750. 800.] test eval: Mean squared error: 1.7638888888888888 Correlation coefficient: 0.41649656391752043 Coefficient of determination (R-squared score, R2 score): 0.05135387488328669 train eval: Mean squared error: 1.1820175438596492 Correlation coefficient: 0.5136147793934669 Coefficient of determination (R-squared score, R2 score): 0.17104486549868902
---- ---- ---- class_num = 816 Number of unique elements: 264 [ 0. 51. 102. 153. 204. 255. 306. 357. 408. 459. 510. 561. 612. 663. 714. 765. 816.] test eval: Mean squared error: 1.8611111111111112 Correlation coefficient: 0.40116685879758923 Coefficient of determination (R-squared score, R2 score): -0.0009337068160597539 train eval: Mean squared error: 1.222953216374269 Correlation coefficient: 0.49884293549266023 Coefficient of determination (R-squared score, R2 score): 0.14233646257223664
---- ---- ---- class_num = 832 Number of unique elements: 268 [ 0. 52. 104. 156. 208. 260. 312. 364. 416. 468. 520. 572. 624. 676. 728. 780. 832.] test eval: Mean squared error: 1.6666666666666667 Correlation coefficient: 0.4598778678854598 Coefficient of determination (R-squared score, R2 score): 0.10364145658263302 train eval: Mean squared error: 1.2587719298245614 Correlation coefficient: 0.4911647502658023 Coefficient of determination (R-squared score, R2 score): 0.1172166100115909
---- ---- ---- class_num = 848 Number of unique elements: 268 [ 0. 53. 106. 159. 212. 265. 318. 371. 424. 477. 530. 583. 636. 689. 742. 795. 848.] test eval: Mean squared error: 1.5972222222222223 Correlation coefficient: 0.48623577949191543 Coefficient of determination (R-squared score, R2 score): 0.1409897292250234 train eval: Mean squared error: 1.2171052631578947 Correlation coefficient: 0.507322494722587 Coefficient of determination (R-squared score, R2 score): 0.14643766299030125
---- ---- ---- class_num = 864 Number of unique elements: 271 [ 0. 54. 108. 162. 216. 270. 324. 378. 432. 486. 540. 594. 648. 702. 756. 810. 864.] test eval: Mean squared error: 1.8194444444444444 Correlation coefficient: 0.4092964857152734 Coefficient of determination (R-squared score, R2 score): 0.02147525676937445 train eval: Mean squared error: 1.2163742690058479 Correlation coefficient: 0.49532048607072776 Coefficient of determination (R-squared score, R2 score): 0.14695031304255934
---- ---- ---- class_num = 880 Number of unique elements: 277 [ 0. 55. 110. 165. 220. 275. 330. 385. 440. 495. 550. 605. 660. 715. 770. 825. 880.] test eval: Mean squared error: 1.6805555555555556 Correlation coefficient: 0.445963575868674 Coefficient of determination (R-squared score, R2 score): 0.09617180205415499 train eval: Mean squared error: 1.2288011695906433 Correlation coefficient: 0.4960515437335157 Coefficient of determination (R-squared score, R2 score): 0.13823526215417203
---- ---- ---- class_num = 896 Number of unique elements: 277 [ 0. 56. 112. 168. 224. 280. 336. 392. 448. 504. 560. 616. 672. 728. 784. 840. 896.] test eval: Mean squared error: 1.7083333333333333 Correlation coefficient: 0.44557269775520997 Coefficient of determination (R-squared score, R2 score): 0.08123249299719892 train eval: Mean squared error: 1.212719298245614 Correlation coefficient: 0.4852675326800607 Coefficient of determination (R-squared score, R2 score): 0.1495135633038498
---- ---- ---- class_num = 912 Number of unique elements: 284 [ 0. 57. 114. 171. 228. 285. 342. 399. 456. 513. 570. 627. 684. 741. 798. 855. 912.] test eval: Mean squared error: 2.0694444444444446 Correlation coefficient: 0.32437417455848905 Coefficient of determination (R-squared score, R2 score): -0.11297852474323067 train eval: Mean squared error: 1.2178362573099415 Correlation coefficient: 0.4961835687110365 Coefficient of determination (R-squared score, R2 score): 0.14592501293804316
---- ---- ---- class_num = 928 Number of unique elements: 290 [ 0. 58. 116. 174. 232. 290. 348. 406. 464. 522. 580. 638. 696. 754. 812. 870. 928.] test eval: Mean squared error: 1.7777777777777777 Correlation coefficient: 0.4278514028529646 Coefficient of determination (R-squared score, R2 score): 0.043884220354808545 train eval: Mean squared error: 1.1871345029239766 Correlation coefficient: 0.5127393612161735 Coefficient of determination (R-squared score, R2 score): 0.1674563151328825
---- ---- ---- class_num = 944 Number of unique elements: 292 [ 0. 59. 118. 177. 236. 295. 354. 413. 472. 531. 590. 649. 708. 767. 826. 885. 944.] test eval: Mean squared error: 1.7777777777777777 Correlation coefficient: 0.4218517909543616 Coefficient of determination (R-squared score, R2 score): 0.043884220354808545 train eval: Mean squared error: 1.215643274853801 Correlation coefficient: 0.48843955167584124 Coefficient of determination (R-squared score, R2 score): 0.14746296309481743
---- ---- ---- class_num = 960 Number of unique elements: 292 [ 0. 60. 120. 180. 240. 300. 360. 420. 480. 540. 600. 660. 720. 780. 840. 900. 960.] test eval: Mean squared error: 1.9444444444444444 Correlation coefficient: 0.3798391616545401 Coefficient of determination (R-squared score, R2 score): -0.045751633986928164 train eval: Mean squared error: 1.2412280701754386 Correlation coefficient: 0.4907642318916595 Coefficient of determination (R-squared score, R2 score): 0.12952021126578472
---- ---- ---- class_num = 976 Number of unique elements: 300 [ 0. 61. 122. 183. 244. 305. 366. 427. 488. 549. 610. 671. 732. 793. 854. 915. 976.] test eval: Mean squared error: 1.6111111111111112 Correlation coefficient: 0.4643180308016195 Coefficient of determination (R-squared score, R2 score): 0.13352007469654525 train eval: Mean squared error: 1.1717836257309941 Correlation coefficient: 0.5032131755549937 Coefficient of determination (R-squared score, R2 score): 0.17822196623030206
---- ---- ---- class_num = 992 Number of unique elements: 302 [ 0. 62. 124. 186. 248. 310. 372. 434. 496. 558. 620. 682. 744. 806. 868. 930. 992.] test eval: Mean squared error: 1.75 Correlation coefficient: 0.4425810719356941 Coefficient of determination (R-squared score, R2 score): 0.05882352941176472 train eval: Mean squared error: 1.2141812865497077 Correlation coefficient: 0.4924229665220838 Coefficient of determination (R-squared score, R2 score): 0.14848826319933361
---- ---- ---- class_num = 1008 Number of unique elements: 306 [ 0. 63. 126. 189. 252. 315. 378. 441. 504. 567. 630. 693. 756. 819. 882. 945. 1008.] test eval: Mean squared error: 1.9027777777777777 Correlation coefficient: 0.3949865893448851 Coefficient of determination (R-squared score, R2 score): -0.023342670401493848 train eval: Mean squared error: 1.277046783625731 Correlation coefficient: 0.49003852921054897 Coefficient of determination (R-squared score, R2 score): 0.10440035870513897
---- ---- ---- class_num = 1024 Number of unique elements: 304 [ 0. 64. 128. 192. 256. 320. 384. 448. 512. 576. 640. 704. 768. 832. 896. 960. 1024.] test eval: Mean squared error: 1.9027777777777777 Correlation coefficient: 0.3889222341312982 Coefficient of determination (R-squared score, R2 score): -0.023342670401493848 train eval: Mean squared error: 1.2185672514619883 Correlation coefficient: 0.49090513620356135 Coefficient of determination (R-squared score, R2 score): 0.14541236288578518
---- ---- ---- class_num = 1040 Number of unique elements: 312 [ 0. 65. 130. 195. 260. 325. 390. 455. 520. 585. 650. 715. 780. 845. 910. 975. 1040.] test eval: Mean squared error: 1.9444444444444444 Correlation coefficient: 0.3748621129653715 Coefficient of determination (R-squared score, R2 score): -0.045751633986928164 train eval: Mean squared error: 1.2492690058479532 Correlation coefficient: 0.5059758217555854 Coefficient of determination (R-squared score, R2 score): 0.12388106069094584
---- ---- ---- class_num = 1056 Number of unique elements: 316 [ 0. 66. 132. 198. 264. 330. 396. 462. 528. 594. 660. 726. 792. 858. 924. 990. 1056.] test eval: Mean squared error: 1.9305555555555556 Correlation coefficient: 0.3864606549319353 Coefficient of determination (R-squared score, R2 score): -0.03828197945845013 train eval: Mean squared error: 1.2244152046783625 Correlation coefficient: 0.4953468680585596 Coefficient of determination (R-squared score, R2 score): 0.14131116246772057
---- ---- ---- class_num = 1072 Number of unique elements: 320 [ 0. 67. 134. 201. 268. 335. 402. 469. 536. 603. 670. 737. 804. 871. 938. 1005. 1072.] test eval: Mean squared error: 1.7777777777777777 Correlation coefficient: 0.41694524488161216 Coefficient of determination (R-squared score, R2 score): 0.043884220354808545 train eval: Mean squared error: 1.1812865497076024 Correlation coefficient: 0.5099181789430145 Coefficient of determination (R-squared score, R2 score): 0.17155751555094712
---- ---- ---- class_num = 1088 Number of unique elements: 318 [ 0. 68. 136. 204. 272. 340. 408. 476. 544. 612. 680. 748. 816. 884. 952. 1020. 1088.] test eval: Mean squared error: 1.8194444444444444 Correlation coefficient: 0.41074765891222537 Coefficient of determination (R-squared score, R2 score): 0.02147525676937445 train eval: Mean squared error: 1.1951754385964912 Correlation coefficient: 0.5096671321693497 Coefficient of determination (R-squared score, R2 score): 0.16181716455804362
---- ---- ---- class_num = 1104 Number of unique elements: 323 [ 0. 69. 138. 207. 276. 345. 414. 483. 552. 621. 690. 759. 828. 897. 966. 1035. 1104.] test eval: Mean squared error: 1.7777777777777777 Correlation coefficient: 0.4258446607339278 Coefficient of determination (R-squared score, R2 score): 0.043884220354808545 train eval: Mean squared error: 1.2105263157894737 Correlation coefficient: 0.4975896604428568 Coefficient of determination (R-squared score, R2 score): 0.15105151346062395
---- ---- ---- class_num = 1120 Number of unique elements: 325 [ 0. 70. 140. 210. 280. 350. 420. 490. 560. 630. 700. 770. 840. 910. 980. 1050. 1120.] test eval: Mean squared error: 1.7638888888888888 Correlation coefficient: 0.4109044228612891 Coefficient of determination (R-squared score, R2 score): 0.05135387488328669 train eval: Mean squared error: 1.206140350877193 Correlation coefficient: 0.5047438378997717 Coefficient of determination (R-squared score, R2 score): 0.1541274137741725
---- ---- ---- class_num = 1136 Number of unique elements: 331 [ 0. 71. 142. 213. 284. 355. 426. 497. 568. 639. 710. 781. 852. 923. 994. 1065. 1136.] test eval: Mean squared error: 1.625 Correlation coefficient: 0.470225484684118 Coefficient of determination (R-squared score, R2 score): 0.12605042016806722 train eval: Mean squared error: 1.1717836257309941 Correlation coefficient: 0.508497189330375 Coefficient of determination (R-squared score, R2 score): 0.17822196623030206
---- ---- ---- class_num = 1152 Number of unique elements: 339 [ 0. 72. 144. 216. 288. 360. 432. 504. 576. 648. 720. 792. 864. 936. 1008. 1080. 1152.] test eval: Mean squared error: 1.9722222222222223 Correlation coefficient: 0.3644573237131406 Coefficient of determination (R-squared score, R2 score): -0.06069094304388423 train eval: Mean squared error: 1.3179824561403508 Correlation coefficient: 0.47299186953477274 Coefficient of determination (R-squared score, R2 score): 0.07569195577868659
---- ---- ---- class_num = 1168 Number of unique elements: 336 [ 0. 73. 146. 219. 292. 365. 438. 511. 584. 657. 730. 803. 876. 949. 1022. 1095. 1168.] test eval: Mean squared error: 2.0416666666666665 Correlation coefficient: 0.36481486423763915 Coefficient of determination (R-squared score, R2 score): -0.0980392156862746 train eval: Mean squared error: 1.2521929824561404 Correlation coefficient: 0.48716306635251094 Coefficient of determination (R-squared score, R2 score): 0.1218304604819136
---- ---- ---- class_num = 1184 Number of unique elements: 342 [ 0. 74. 148. 222. 296. 370. 444. 518. 592. 666. 740. 814. 888. 962. 1036. 1110. 1184.] test eval: Mean squared error: 1.7916666666666667 Correlation coefficient: 0.4308515586693371 Coefficient of determination (R-squared score, R2 score): 0.036414565826330514 train eval: Mean squared error: 1.1871345029239766 Correlation coefficient: 0.513645988436496 Coefficient of determination (R-squared score, R2 score): 0.1674563151328825
---- ---- ---- class_num = 1200 Number of unique elements: 346 [ 0. 75. 150. 225. 300. 375. 450. 525. 600. 675. 750. 825. 900. 975. 1050. 1125. 1200.] test eval: Mean squared error: 1.8472222222222223 Correlation coefficient: 0.40014040511229637 Coefficient of determination (R-squared score, R2 score): 0.006535947712418277 train eval: Mean squared error: 1.2675438596491229 Correlation coefficient: 0.4921374695750742 Coefficient of determination (R-squared score, R2 score): 0.11106480938449392
---- ---- ---- class_num = 1216 Number of unique elements: 347 [ 0. 76. 152. 228. 304. 380. 456. 532. 608. 684. 760. 836. 912. 988. 1064. 1140. 1216.] test eval: Mean squared error: 1.8055555555555556 Correlation coefficient: 0.4095234117078239 Coefficient of determination (R-squared score, R2 score): 0.028944911297852483 train eval: Mean squared error: 1.185672514619883 Correlation coefficient: 0.5128907976324513 Coefficient of determination (R-squared score, R2 score): 0.16848161523739857
---- ---- ---- class_num = 1232 Number of unique elements: 347 [ 0. 77. 154. 231. 308. 385. 462. 539. 616. 693. 770. 847. 924. 1001. 1078. 1155. 1232.] test eval: Mean squared error: 1.7083333333333333 Correlation coefficient: 0.42345298307322854 Coefficient of determination (R-squared score, R2 score): 0.08123249299719892 train eval: Mean squared error: 1.2171052631578947 Correlation coefficient: 0.4948718969820021 Coefficient of determination (R-squared score, R2 score): 0.14643766299030125
---- ---- ---- class_num = 1248 Number of unique elements: 352 [ 0. 78. 156. 234. 312. 390. 468. 546. 624. 702. 780. 858. 936. 1014. 1092. 1170. 1248.] test eval: Mean squared error: 1.9722222222222223 Correlation coefficient: 0.35624894256814954 Coefficient of determination (R-squared score, R2 score): -0.06069094304388423 train eval: Mean squared error: 1.185672514619883 Correlation coefficient: 0.5086345245665878 Coefficient of determination (R-squared score, R2 score): 0.16848161523739857
---- ---- ---- class_num = 1264 Number of unique elements: 362 [ 0. 79. 158. 237. 316. 395. 474. 553. 632. 711. 790. 869. 948. 1027. 1106. 1185. 1264.] test eval: Mean squared error: 1.9305555555555556 Correlation coefficient: 0.3762051253359772 Coefficient of determination (R-squared score, R2 score): -0.03828197945845013 train eval: Mean squared error: 1.141812865497076 Correlation coefficient: 0.5220215043135258 Coefficient of determination (R-squared score, R2 score): 0.1992406183728832
---- ---- ---- class_num = 1280 Number of unique elements: 356 [ 0. 80. 160. 240. 320. 400. 480. 560. 640. 720. 800. 880. 960. 1040. 1120. 1200. 1280.] test eval: Mean squared error: 1.8055555555555556 Correlation coefficient: 0.42744406961189996 Coefficient of determination (R-squared score, R2 score): 0.028944911297852483 train eval: Mean squared error: 1.3296783625730995 Correlation coefficient: 0.46742597553862225 Coefficient of determination (R-squared score, R2 score): 0.06748955494255737
---- ---- ---- class_num = 1296 Number of unique elements: 366 [ 0. 81. 162. 243. 324. 405. 486. 567. 648. 729. 810. 891. 972. 1053. 1134. 1215. 1296.] test eval: Mean squared error: 2.0694444444444446 Correlation coefficient: 0.36105378580232217 Coefficient of determination (R-squared score, R2 score): -0.11297852474323067 train eval: Mean squared error: 1.2083333333333333 Correlation coefficient: 0.500632638407923 Coefficient of determination (R-squared score, R2 score): 0.15258946361739822
---- ---- ---- class_num = 1312 Number of unique elements: 368 [ 0. 82. 164. 246. 328. 410. 492. 574. 656. 738. 820. 902. 984. 1066. 1148. 1230. 1312.] test eval: Mean squared error: 1.7916666666666667 Correlation coefficient: 0.4015119589281471 Coefficient of determination (R-squared score, R2 score): 0.036414565826330514 train eval: Mean squared error: 1.161549707602339 Correlation coefficient: 0.5263855207662416 Coefficient of determination (R-squared score, R2 score): 0.18539906696191522
---- ---- ---- class_num = 1328 Number of unique elements: 370 [ 0. 83. 166. 249. 332. 415. 498. 581. 664. 747. 830. 913. 996. 1079. 1162. 1245. 1328.] test eval: Mean squared error: 1.75 Correlation coefficient: 0.42016714111016656 Coefficient of determination (R-squared score, R2 score): 0.05882352941176472 train eval: Mean squared error: 1.226608187134503 Correlation coefficient: 0.4903677851168673 Coefficient of determination (R-squared score, R2 score): 0.1397732123109463
---- ---- ---- class_num = 1344 Number of unique elements: 372 [ 0. 84. 168. 252. 336. 420. 504. 588. 672. 756. 840. 924. 1008. 1092. 1176. 1260. 1344.] test eval: Mean squared error: 1.875 Correlation coefficient: 0.397008286950533 Coefficient of determination (R-squared score, R2 score): -0.008403361344537785 train eval: Mean squared error: 1.144736842105263 Correlation coefficient: 0.5209375365562346 Coefficient of determination (R-squared score, R2 score): 0.19719001816385096
---- ---- ---- class_num = 1360 Number of unique elements: 371 [ 0. 85. 170. 255. 340. 425. 510. 595. 680. 765. 850. 935. 1020. 1105. 1190. 1275. 1360.] test eval: Mean squared error: 1.6805555555555556 Correlation coefficient: 0.4411674610445075 Coefficient of determination (R-squared score, R2 score): 0.09617180205415499 train eval: Mean squared error: 1.2207602339181287 Correlation coefficient: 0.4877169234835959 Coefficient of determination (R-squared score, R2 score): 0.14387441272901091
---- ---- ---- class_num = 1376 Number of unique elements: 377 [ 0. 86. 172. 258. 344. 430. 516. 602. 688. 774. 860. 946. 1032. 1118. 1204. 1290. 1376.] test eval: Mean squared error: 1.8888888888888888 Correlation coefficient: 0.4096210940636037 Coefficient of determination (R-squared score, R2 score): -0.015873015873015817 train eval: Mean squared error: 1.1864035087719298 Correlation coefficient: 0.5182179271486073 Coefficient of determination (R-squared score, R2 score): 0.1679689651851406
---- ---- ---- class_num = 1392 Number of unique elements: 383 [ 0. 87. 174. 261. 348. 435. 522. 609. 696. 783. 870. 957. 1044. 1131. 1218. 1305. 1392.] test eval: Mean squared error: 2.138888888888889 Correlation coefficient: 0.31462284154851966 Coefficient of determination (R-squared score, R2 score): -0.15032679738562083 train eval: Mean squared error: 1.1980994152046784 Correlation coefficient: 0.5200547772401144 Coefficient of determination (R-squared score, R2 score): 0.15976656434901126
---- ---- ---- class_num = 1408 Number of unique elements: 382 [ 0. 88. 176. 264. 352. 440. 528. 616. 704. 792. 880. 968. 1056. 1144. 1232. 1320. 1408.] test eval: Mean squared error: 2.0416666666666665 Correlation coefficient: 0.35698982974735893 Coefficient of determination (R-squared score, R2 score): -0.0980392156862746 train eval: Mean squared error: 1.2719298245614035 Correlation coefficient: 0.4777021549359274 Coefficient of determination (R-squared score, R2 score): 0.1079889090709455
---- ---- ---- class_num = 1424 Number of unique elements: 386 [ 0. 89. 178. 267. 356. 445. 534. 623. 712. 801. 890. 979. 1068. 1157. 1246. 1335. 1424.] test eval: Mean squared error: 1.7638888888888888 Correlation coefficient: 0.427251444912582 Coefficient of determination (R-squared score, R2 score): 0.05135387488328669 train eval: Mean squared error: 1.1001461988304093 Correlation coefficient: 0.5432958222364069 Coefficient of determination (R-squared score, R2 score): 0.22846167135159368
---- ---- ---- class_num = 1440 Number of unique elements: 396 [ 0. 90. 180. 270. 360. 450. 540. 630. 720. 810. 900. 990. 1080. 1170. 1260. 1350. 1440.] test eval: Mean squared error: 1.8194444444444444 Correlation coefficient: 0.39540056450390443 Coefficient of determination (R-squared score, R2 score): 0.02147525676937445 train eval: Mean squared error: 1.118421052631579 Correlation coefficient: 0.5287861334997481 Coefficient of determination (R-squared score, R2 score): 0.21564542004514176
---- ---- ---- class_num = 1456 Number of unique elements: 392 [ 0. 91. 182. 273. 364. 455. 546. 637. 728. 819. 910. 1001. 1092. 1183. 1274. 1365. 1456.] test eval: Mean squared error: 1.8194444444444444 Correlation coefficient: 0.39722438724914694 Coefficient of determination (R-squared score, R2 score): 0.02147525676937445 train eval: Mean squared error: 1.182748538011696 Correlation coefficient: 0.508774567698493 Coefficient of determination (R-squared score, R2 score): 0.17053221544643093
---- ---- ---- class_num = 1472 Number of unique elements: 396 [ 0. 92. 184. 276. 368. 460. 552. 644. 736. 828. 920. 1012. 1104. 1196. 1288. 1380. 1472.] test eval: Mean squared error: 1.9166666666666667 Correlation coefficient: 0.3937306173126693 Coefficient of determination (R-squared score, R2 score): -0.03081232492997188 train eval: Mean squared error: 1.2295321637426901 Correlation coefficient: 0.5070049803704809 Coefficient of determination (R-squared score, R2 score): 0.13772261210191394
---- ---- ---- class_num = 1488 Number of unique elements: 402 [ 0. 93. 186. 279. 372. 465. 558. 651. 744. 837. 930. 1023. 1116. 1209. 1302. 1395. 1488.] test eval: Mean squared error: 1.8333333333333333 Correlation coefficient: 0.4165054821991276 Coefficient of determination (R-squared score, R2 score): 0.014005602240896309 train eval: Mean squared error: 1.2054093567251463 Correlation coefficient: 0.511688518217734 Coefficient of determination (R-squared score, R2 score): 0.15464006382643058
---- ---- ---- class_num = 1504 Number of unique elements: 404 [ 0. 94. 188. 282. 376. 470. 564. 658. 752. 846. 940. 1034. 1128. 1222. 1316. 1410. 1504.] test eval: Mean squared error: 1.8888888888888888 Correlation coefficient: 0.39994096593713974 Coefficient of determination (R-squared score, R2 score): -0.015873015873015817 train eval: Mean squared error: 1.2317251461988303 Correlation coefficient: 0.5123292285161234 Coefficient of determination (R-squared score, R2 score): 0.13618466194513978
---- ---- ---- class_num = 1520 Number of unique elements: 404 [ 0. 95. 190. 285. 380. 475. 570. 665. 760. 855. 950. 1045. 1140. 1235. 1330. 1425. 1520.] test eval: Mean squared error: 1.8611111111111112 Correlation coefficient: 0.38855556069841796 Coefficient of determination (R-squared score, R2 score): -0.0009337068160597539 train eval: Mean squared error: 1.1527777777777777 Correlation coefficient: 0.5105411967042561 Coefficient of determination (R-squared score, R2 score): 0.19155086758901207
---- ---- ---- class_num = 1536 Number of unique elements: 408 [ 0. 96. 192. 288. 384. 480. 576. 672. 768. 864. 960. 1056. 1152. 1248. 1344. 1440. 1536.] test eval: Mean squared error: 2.2083333333333335 Correlation coefficient: 0.3087692163592721 Coefficient of determination (R-squared score, R2 score): -0.1876750700280112 train eval: Mean squared error: 1.246345029239766 Correlation coefficient: 0.5012151401352187 Coefficient of determination (R-squared score, R2 score): 0.1259316608999782
---- ---- ---- class_num = 1552 Number of unique elements: 405 [ 0. 97. 194. 291. 388. 485. 582. 679. 776. 873. 970. 1067. 1164. 1261. 1358. 1455. 1552.] test eval: Mean squared error: 1.7222222222222223 Correlation coefficient: 0.4351681733072561 Coefficient of determination (R-squared score, R2 score): 0.07376283846872078 train eval: Mean squared error: 1.1944444444444444 Correlation coefficient: 0.5138497389431315 Coefficient of determination (R-squared score, R2 score): 0.16232981461030171
---- ---- ---- class_num = 1568 Number of unique elements: 413 [ 0. 98. 196. 294. 392. 490. 588. 686. 784. 882. 980. 1078. 1176. 1274. 1372. 1470. 1568.] test eval: Mean squared error: 1.9305555555555556 Correlation coefficient: 0.3595284314783199 Coefficient of determination (R-squared score, R2 score): -0.03828197945845013 train eval: Mean squared error: 1.1264619883040936 Correlation coefficient: 0.5242889582886737 Coefficient of determination (R-squared score, R2 score): 0.21000626947030288
---- ---- ---- class_num = 1584 Number of unique elements: 417 [ 0. 99. 198. 297. 396. 495. 594. 693. 792. 891. 990. 1089. 1188. 1287. 1386. 1485. 1584.] test eval: Mean squared error: 1.9722222222222223 Correlation coefficient: 0.38532134184783023 Coefficient of determination (R-squared score, R2 score): -0.06069094304388423 train eval: Mean squared error: 1.219298245614035 Correlation coefficient: 0.49697530607501067 Coefficient of determination (R-squared score, R2 score): 0.1448997128335271
---- ---- ---- class_num = 1600 Number of unique elements: 415 [ 0. 100. 200. 300. 400. 500. 600. 700. 800. 900. 1000. 1100. 1200. 1300. 1400. 1500. 1600.] test eval: Mean squared error: 1.9166666666666667 Correlation coefficient: 0.39373061731266834 Coefficient of determination (R-squared score, R2 score): -0.03081232492997188 train eval: Mean squared error: 1.2412280701754386 Correlation coefficient: 0.497512882424363 Coefficient of determination (R-squared score, R2 score): 0.12952021126578472
# plot the trend figures of mse, correlation, and r2
# Create a figure and subplots
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(8, 12))
# Plot MSE
ax1.plot(class_num_array, mse_test_list, label='MSE (Test)')
ax1.plot(class_num_array, mse_train_list, label='MSE (Train)')
ax1.set_ylabel('MSE')
ax1.set_xlabel('Original Class Number')
ax1.set_title(f'MSE Curve (reduced class num is {reduced_class_num})')
ax1.legend()
# Plot Correlation
ax2.plot(class_num_array, correlation_test_list, label='Correlation (Test)')
ax2.plot(class_num_array, correlation_train_list, label='Correlation (Train)')
ax2.set_ylabel('Correlation')
ax2.set_xlabel('Original Class Number')
ax2.set_title(f'Correlation Curve (reduced class num is {reduced_class_num})')
ax2.legend()
# Plot R-squared
ax3.plot(class_num_array, r_squared_test_list, label='R-squared (Test)')
ax3.plot(class_num_array, r_squared_train_list, label='R-squared (Train)')
ax3.set_ylabel('R-squared')
ax3.set_xlabel('Original Class Number')
ax3.set_title(f'R-squared Curve (reduced class num is {reduced_class_num})')
ax3.legend()
# Increase the vertical spacing between subplots
plt.subplots_adjust(hspace=0.5)
# Adjust tick, label, title, and legend font sizes
plt.rcParams.update({'font.size': 12})
ax1.tick_params(labelsize=10)
ax2.tick_params(labelsize=10)
ax3.tick_params(labelsize=10)
# Save the figure
plt.savefig(f'mse_correlation_r2_trend_curve_reduced_eval_reduced_class_num_{reduced_class_num}.png', bbox_inches='tight')
# Show the figure
plt.show()
# Convert r_squared_test_list to a NumPy array
r_squared_test_array = np.array(r_squared_test_list)
# Find the index of the maximum value
max_index = np.argmax(r_squared_test_array)
# Get the corresponding class_num value
max_class_num = class_num_array[max_index]
# Print the index and corresponding class_num
print("Max Index:", max_index)
print("Max Original Class Num:", max_class_num)
Max Index: 10 Max Original Class Num: 176
# batch download the plotted figures
# uncomment the code below to download figures if needed
'''
import glob
folder_path = '.'
file_prefix = 'Comparison of Sorted Predictions and Sorted Ground Truth (Logistic Linear Regression Reduced Evaluation'
# file_prefix = 'Comparison of Sorted Predictions and Sorted Ground Truth'
# Use glob to find all files with the given prefix in the folder
matching_files = glob.glob(f"{folder_path}/{file_prefix}*")
# print(matching_files)
# # Print the matching file names
# for file_path in matching_files:
# print(file_path)
import zipfile
zip_filename = 'files.zip'
with zipfile.ZipFile(zip_filename, 'w') as zipf:
# Add files to the zip file
for file_path in matching_files:
zipf.write(file_path)
from google.colab import files
files.download(zip_filename)
'''
balanced weights don't improve the fitting, but make it worse.
# independent data
x = group_satcked_green
class_num = 48
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# print(np.max(y), np.min(y))
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
# print(intervals)
# Digitize the array to get the indices of the intervals
y_train = np.digitize(y_train, intervals) - 1
y_test = np.digitize(y_test, intervals) - 1
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
# to see unique elements (see if we have all 0, 1,..., class_num-1 classes, better close to all)
unique_elements = np.unique(y_train)
print("Unique elements:", unique_elements)
print("Number of unique elements:", len(unique_elements))
x_train shape: (1368, 14) y_train shape: (1368,) x_test shape: (72, 14) y_test shape: (72,) Unique elements: [ 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 29 30 33 34 35 37 42 47] Number of unique elements: 30
# fit
model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, class_weight='balanced', multi_class='multinomial')
fit_result = model.fit(x_train, y_train)
print(fit_result.intercept_.shape, fit_result.coef_.shape)
# predict
# Use the trained model to make predictions
y_pred = model.predict(x_test)
# Alternatively, you can get the predicted probabilities for each class
y_prob = model.predict_proba(x_test)
# Print the predicted class labels
print(y_pred, y_test)
print(y_pred.shape, y_test.shape)
# Print the predicted probabilities
# print(y_prob)
(30,) (30, 14) [ 7 7 19 9 8 19 29 25 14 26 14 19 35 13 19 26 13 12 20 9 22 14 11 20 14 37 9 25 29 8 18 25 8 12 21 10 19 26 8 19 9 10 26 26 24 11 14 13 8 24 26 22 21 19 16 10 13 14 18 20 20 19 11 7 7 8 20 9 8 20 29 22] [15 18 16 12 15 13 19 18 16 18 16 15 26 17 18 15 12 17 25 0 17 17 15 13 14 26 18 16 13 13 16 17 14 15 13 12 14 18 17 16 18 12 17 30 19 15 15 18 15 27 14 17 17 16 17 15 15 14 16 17 21 14 16 17 15 19 13 7 20 17 16 18] (72,) (72,)
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)
cm = confusion_matrix(y_test, y_pred)
print("Confusion Matrix:")
print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
plot_comparison(y_test, y_pred, 'Logistic Linear Regression balanced weights, Test Set')
Accuracy: 0.027777777777777776 Confusion Matrix: [[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 1 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 1 0 0 0] [0 0 1 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0 0] [0 2 2 0 1 2 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0] [0 0 0 0 0 1 0 0 2 0 0 0 2 3 0 0 0 0 1 0 0 1 0 0 0] [0 1 1 0 0 0 1 1 1 0 1 0 0 0 2 1 2 0 1 1 0 0 0 0 0] [0 1 0 2 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 2 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]] Correlation coefficient: 0.4433163758712943
# predict on train
# Use the trained model to make predictions
y_pred_ = model.predict(x_train)
# Alternatively, you can get the predicted probabilities for each class
y_prob_ = model.predict_proba(x_train)
accuracy = accuracy_score(y_train, y_pred_)
print("Accuracy:", accuracy)
cm = confusion_matrix(y_train, y_pred_)
print("Confusion Matrix:")
print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
plot_comparison(y_train, y_pred_, 'Logistic Linear Regression balanced weights, Train Set')
Accuracy: 0.07309941520467836 Confusion Matrix: [[ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 1 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 4 6 2 3 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0] [ 0 3 6 2 2 5 0 1 2 0 0 1 2 1 0 2 1 1 0 0 2 0 2 0 0 0 0 0 0 0] [ 0 2 14 7 9 6 4 3 5 3 0 1 0 0 4 0 1 1 0 2 4 0 1 0 0 0 0 0 0 0] [ 0 2 10 15 18 8 3 7 6 2 2 1 0 6 4 0 2 0 1 3 8 0 3 0 0 0 0 0 0 0] [ 0 9 15 20 18 16 3 9 11 9 2 3 2 5 8 4 5 2 1 6 8 1 7 0 0 0 0 0 0 0] [ 1 4 14 17 16 17 5 6 12 11 4 4 4 6 16 8 10 0 1 7 14 2 9 0 0 0 0 0 0 0] [ 0 11 16 6 19 14 3 12 16 6 7 4 6 8 21 7 13 1 3 5 18 2 8 0 0 0 0 0 0 0] [ 0 7 10 13 13 7 5 11 7 2 2 4 4 5 20 10 9 4 3 6 10 2 16 0 0 0 0 0 0 0] [ 0 1 3 5 5 4 1 9 4 3 1 2 4 5 20 8 9 4 2 9 11 1 14 2 0 0 2 0 1 0] [ 0 2 6 6 2 2 1 3 1 3 2 0 2 6 15 10 9 4 1 8 11 1 7 0 0 0 0 0 0 1] [ 2 1 5 2 1 0 0 5 4 0 2 0 1 2 8 5 5 1 3 6 6 0 5 1 0 1 2 0 0 0] [ 0 1 0 0 2 1 0 4 0 0 0 0 0 0 7 3 3 3 0 3 4 0 2 0 0 0 0 0 0 0] [ 0 0 1 1 0 0 0 1 1 0 0 0 0 2 1 1 1 0 0 2 1 0 3 1 0 0 1 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 3 0 0 2 3 2 2 0 0 0 1 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 2 3 0 0 0 0 0 0 0 0] [ 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 2 0 0 1] [ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 1 1 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]] Correlation coefficient: 0.4452289383051512
